text:
Publication number | US5610847 A |
Publication type | Grant |
Application number | US 08/331,186 |
Publication date | Mar 11, 1997 |
Filing date | Oct 28, 1994 |
Priority date | Oct 28, 1994 |
Fee status | Paid |
Also published as | DE69532509D1, DE69532509T2, EP0788607A1, EP0788607B1, WO1996013729A1 |
Publication number | 08331186, 331186, US 5610847 A, US 5610847A, US-A-5610847, US5610847 A, US5610847A |
Inventors | Kenneth S. Kundert |
Original Assignee | Cadence Design Systems, Inc. |
Export Citation | BiBTeX, EndNote, RefMan |
Patent Citations (11), Referenced by (8), Classifications (11), Legal Events (4) | |
External Links: USPTO, USPTO Assignment, Espacenet | |
1. Field of the Invention
The present invention is a method and apparatus for determining the frequency components of a waveform that is sampled at a discrete set of times, and more particularly, for determining the Fourier coefficients of the output waveform of a circuit or a simulator, based on samples of the output waveform taken at selected time intervals.
2. Related Art
In order to characterize the behavior of circuits and electronic systems, it is often useful to analyze the frequency components of the output waveform that is generated by the circuit or electronic system. The output waveform may be generated by an actual circuit or electronic system, but more typically it is generated by a circuit simulator. Typically, the simulator is driven by a reference signal at a fundamental frequency and the amplitudes of the various harmonic frequencies in the output waveform are identified by means of Fourier analysis, whereby the time-dependent output waveform of the circuit or system is transformed into a frequency-domain function. The amplitude of the frequency domain function at a given frequency indicates the relative contribution of the frequency to the output waveform. The results of Fourier analysis are typically represented as a series of Fourier coefficients, the magnitudes of which indicate the distribution of energy in the output waveform among the fundamental and harmonic frequencies.
Conventional Fourier analyzers typically detect the actual or simulated output waveform at uniform time intervals, (the sampling rate) and the integral transforth that relates the Fourier coefficient to the detected output waveform is approximated by a discrete Fourier series. The terms of this Fourier series are determined for each time interval using a representative value of the output waveform for the interval and summing each term in the series.
Accurate analysis of the frequency components of an output waveform requires careful selection of the sampling rate, since this rate limits the frequency components that can be resolved in a Fourier analysis. The highest frequency component of a waveform that can be accurately resolved by sampling the waveform every Δ seconds is (2Δ)-1. Frequency components falling outside the range �(2Δ)-1 vary too quickly to be accurately resolved by sampling every Δ seconds. Instead, the energy in these frequency components is added to Fourier coefficients of frequency components within the range. The resulting distortion of the Fourier coefficients is referred to as aliasing and is a major source of errors in the Fourier analysis of broad band output waveforms. For this reason, the sampling rate must be selected so that all frequency components having substantial amplitude in the output waveform fall within the frequency range, �(2Δ)-1. This is a particularly burdensome requirement for output waveforms having broad frequency bands.
Even where the sampling rate is sufficiently fast to resolve substantially all frequency components in an output waveform, discontinuous artifacts in the waveforms generate error components across a broad band of frequencies. Aliasing couples the errors at frequencies outside the range, �(2Δ)-1, into the Fourier coefficients of frequencies within the range. Such error producing discontinuities arise, for example, where an output waveform has not completely settled between analysis cycles, where the wrong period is used for the waveform, or where the waveform computed by a simulator is not completely converged.
Errors in Fourier coefficients may also be introduced through the interpolation method used by a simulator to compute the output waveform. Particularly where the simulator employs a low order interpolation scheme, the time step between adjacent points of the simulated output waveform must be sufficiently small to keep errors in the interpolated output waveform within selected limits. However, small time steps are unnecessary for analyzing the relatively flat portions of the output waveform, and the selected time step typically represents a trade off between accuracy and efficiency in computing the output waveform.
The present invention is a ratiometric Fourier analyzer that resolves the frequency components of an output waveform with increased accuracy and efficiency. The Fourier analyzer of the present invention eliminates errors due to aliasing without increasing the time necessary for analysis. In addition, the rate at which the waveform is sampled varies according to the properties of the output waveform, allowing the Fourier analyzer to sample the output waveform more or less frequently, as required. The ratiometric Fourier analyzer optionally provides a channel for Fourier analyzing the signal that drives the circuit or simulator to generate a reference waveform for checking the accuracy of the analyzer. By normalizing the Fourier coefficients of the output waveform to the amplitude of the fundamental frequency of the reference signal, large signal transfer functions and immitances of the circuit can be computed.
A Ratiometric Fourier analyzer in accordance with the present invention comprises a detector having an input for detecting values of an ouptut waveform at selected times and a processor having a memory that includes a control program. Modules within the control program determine the duration of the selected intervals for detecting values of the output waveform, generate a representation of the output waveform from the detected values, determine a Fourier integral over each interval, and calculate a Fourier coefficient from the Fourier integrals.
The ratiometric Fourier analyzer in accordance with the present invention detects values of an output waveform from a circuit or a system simulator at time intervals selected according to features of the output waveform being analyzed. A functional representation of the output waveform over each of the selected intervals is generated by a module of the control program from the detected values of the output waveform, and a Fourier integral for each frequency of interest is calculated by another module of the control program over the selected interval using this functional representation. The Fourier integrals are then summed over the intervals of the output waveform by a module of the control program to yield the Fourier coefficient at a given frequency for the output waveform. Typically, Fourier coefficients of the output waveform are calculated at the fundamental frequency and for various harmonics of the fundamental frequency.
In a preferred embodiment of the invention, the functional representation of the output waveform is generated by a processor implemented polynomial fitting procedure. Where the output waveform is provided by a simulator, the accuracy of the method may be further improved by employing polynomial fitting procedures to the same order in both the Fourier analyzer and the simulator. The accuracy and efficiency of the method may also be enhanced by selecting the sampling points of the Fourier analyzer at the same time steps used by the simulator to generate the output waveform.
FIG. 1A-C are schematic representation of the output of a conventional Fourier analyzer, exhibiting the effects of aliasing.
FIGS. 2A and 2B are schematic representations of a ratiometric Fourier analyzer in accordance with the present invention, interacting with a circuit and a system simulator, respectively.
FIG. 3 is a flow chart representing the method of the present invention.
FIG. 4 is a schematic diagram of the frequency output of a sigma-delta modulator.
FIG. 5A and 5B are the output of a pulse width modulator and the results of a Fast Fourier Transform analysis of the output, respectively.
Referring to FIG. 1 A, there is shown an output waveform 10 (h(t)) representing an output signal from a circuit or a simulator plotted as a function of time. The sharp curvature of waveform 10 near point 12 indicates that a Fourier transform of output waveform 10 will include contributions from high frequencies. On the other hand, the relative flatness of waveform 10 near point 13 indicates that low frequencies will also be present in the Fourier transform of output waveform 10. Thus, the Fourier transform of output waveform 10 will have non-zero amplitude over a broad range of frequencies.
Referring now to FIG. 1B, there is shown an accurate Fourier transform 20 of output waveform 10. Formally, Fourier transform 20 is obtained from output waveform 10 by means of a Fourier transform integral:
H(f)=∫h(t)e.sup.(2πift) dt. (Eq.1)
Here, h(t) corresponds to output waveform 10 and H(f) corresponds to Fourier transform 20 of output waveform 10.
Conventional Fourier analyzers approximate the integral transform of Eq. 1 with a discrete summation. This discrete Fourier transform (DFT) procedure may yield reasonably accurate results provided the summation is done over finely divided time intervals. In practice, this means that output waveform 10 must be sampled at a high sampling rate. Since high sampling rates increase the time necessary to analyze a waveform, conventional DFT Fourier analyzers typically sample output waveforms at the lowest rate that does not introduce aliasing.
For example, a conventional DFT Fourier transform analyzer analyzes waveform 10 at equal time intervals 30, each having a length, Δ, equal to the inverse of the selected sampling rate. Within each time interval 30, for example at time tk in the kth interval, a value, h.sub.(tk), representative of waveform 10 in the kth interval is multiplied by a factor exp(2 πi fj tk) for each frequency fj of interest. The products are summed over all intervals 30 and multiplied by the uniform width Δ of intervals 30 to yield the Fourier coefficient, Hj, for the frequency, fj.
Hj ≈ΔΣh(tk) exp (2 πifj tk).(Eq. 2)
Typically, the frequencies analyzed are the frequency of the signal that drives the circuit or simulator (fundamental) and its harmonic frequencies.
Aliasing arises in this discrete Fourier transform method when frequency components of waveform 10 fall outside a frequency range that is determined by the sampling interval Δ. This frequency range includes frequencies having absolute values between fN =(2Δ)-1, where negative frequency components are the complex conjugates of positive frequency components. The Fourier amplitudes of any frequencies outside the range, �fN, that contribute to output waveform 10 are folded back and added to the amplitudes of frequencies within this range, �fN.
Referring now to FIG. 1C, there is shown a Fourier transform 21 of output waveform 10 computed by means of Eq. 1, where the width Δ of time intervals 30 is too broad to resolve all significant frequency components of output waveform 10. As a result, significant frequency components exist outside the range �(2Δ)-1 and computed Fourier transform 21 is distorted by alias components 23. Also shown for reference is accurate Fourier transform 20 computed using a shorter time step Δ. The distortion of computed Fourier transform 21 due to alias 23 is indicated by the greater amplitude of computed Fourier transform 21 relative to Fourier transform 20 at frequencies just within the range, �fN, and the absence of contributions to computed Fourier transform 21 from frequencies outside this range.
Even where intervals 30 are selected to be sufficiently short for the frequency components of output waveform 10, errors may be introduced by discontinuities in output waveform 10. Such discontinuities arise when waveform 10 is not exactly periodic due to circuit settling behavior or when the period designated for the reference signal is incorrect. In either case, discontinuities introduce a broad band of frequency components which are likely to exceed the range, �(2Δ)-1. In addition, approximating output waveform 10 over an interval 30 by a fitting function contributes an interpolation error to Fourier coefficients calculated by means of Eq. 2.
Referring now to FIG. 2A, there is shown a schematic representation of a ratiometric Fourier analyzer (RFA) 50 in accordance with the present invention. RFA 50 is shown connected to a simulator 52 which may be programmed to provide output waveforms 10 representative of a wide variety of electronic circuits and systems. RFA 50 further comprises a detector 49 and a processor 51 coupled to a memory 53 in which a control program 55 is stored. Control program 55 controls the detection and analysis of an output waveform 10 as discussed below in conjunction with FIG. 3.
A driving signal 54 is applied to an input 56 of simulator 52 and an output waveform 10 generated by driving signal 54 is coupled from an output 58 of simulator 52 to an input 60 of RFA 50. A control line 64 couples analyzer information, such as the desired fundamental frequency of the analysis, the order of interpolation used by the simulator, and the location of break points, from simulator 52 to RFA 50. A feedback signal line 64 couples information from RFA 50 back to simulator 52 and may be used, for example, to trigger simulator 52 to provide a new data point or to bound the time step. A reference signal line 66 couples driving signal 54 to a second input 68 of RFA 50 so that driving signal 54 may be analyzed by RFA 50 for signal calibration and normalization purposes. For example, where driving signal 54 is a pure sinusoidal signal, it should have a non-zero Fourier coefficient only for the fundamental frequency and zero Fourier coefficients for all other frequencies. Deviations from this result provide a measure of the performance of RFA 50. In addition, the Fourier coefficient of reference signal 54 may be used to determine the gain or immitance as a function of frequency for waveform 10.
Referring now to FIG. 2B, there is shown a schematic diagram in which RFA 50 is connected to receive an output waveform 10 of an actual circuit or electronic system 70. The major difference between the configurations of FIG. 3B and 3A is that feedback signal line 64 is not present in FIG. 3B since electronic system 70 provides a continuous output waveform 10 without triggering by RFA 50.
Referring now to FIG. 3, there is shown a flow chart representing a method 90 implemented by control program 55 operating in conjunction with processor 51 of RFA 50 to analyze output waveforms 10. The flow chart of FIG. 3 is applicable to waveforms 10 whether they are produced by a simulator 52 or an actual electronic system 70. Process 90 begins when an initial value of output waveform 10 is detected 100 at input 60 of RFA 50. Process 90 then waits 110 until a selected interval has passed, at which time a new value of output waveform 10 is retrieved. Procedures for selecting the duration of the wait between retrieval of new values for output waveform 10 are discussed below.
The new value of output waveform 10 is combined with previous values of waveform 10 to generate 130 a functional representation of output waveform 10 between the new value and the preceding value by a curve fitting procedure. The functional representation of output waveform 10 is then used to compute 140 a Fourier integral over the selected interval between the previous and present value of output waveform 10 for each frequency of interest. Use of a functional representation of waveform 10 in the selected interval allows the Fourier integral to be evaluated analytically, eliminating the aliasing problem that arises in discrete Fourier analysis. The computed Fourier integral is then added 150 to the Fourier integrals calculated for the same frequency over previous intervals of output waveform 10.
If the new value is not the last value of output waveform 10, i.e. if output waveform 10 has not been sampled over a full period, T, process 90 branches 160 to wait 110 for the next value of output waveform 10. Otherwise, RFA exits 190 process 90. The details of each of steps 110-190 are discussed below.
The duration of wait 110 may be based on a variety of criteria. For example, the selected intervals between retrieving 120 a new value of output waveform 10 may be uniform, with their duration determined by the expected frequency bandwidth of output waveform 10 or by the period, T, of waveform 10. However, the use of uniform intervals imposes substantial trade-offs between accuracy and efficiency, since short time intervals (high sampling rates) are necessary to accurately transform sections of output waveform 10 having large curvatures (second derivatives) but are unnecessarily short for relatively flat sections of output waveform 10.
In a more preferred embodiment of the present invention, the duration of the selected interval varies according to the behavior of output waveform 10. For example, when output waveform 10 is provided by simulator 52, process 90 waits 110 until simulator 52 computes a new value for output waveform 10. In this case, the selected interval is determined by simulator 52, which computes values for output waveform 10 at shorter intervals as the curvature of output waveform 10 increases and at longer intervals as the curvature of output waveform 10 decreases. For this purpose, simulator 52 may employ error criteria in which the selected interval between calculated values of output waveform 10 decreases as the rate of variation in the values increases. In this case, process 90 waits 110 until a new value is coupled to RFA 50 from output 58 of simulator 52. This method of selecting intervals has the advantage that curve fitting in simulator 52 and RFA 50 can be done to the same level of accuracy without sacrificing efficiency.
In an alternative embodiment of process 90 that is suitable for use with actual circuits or systems 70, RFA 50 can monitor output waveform 10 and exit state 110 when a triggering feature of output waveform 10 is detected. For example, since the accuracy of a curve interpolation scheme employed in a fitting step 130 depends on the curvature of output waveform 10, RFA 50 can monitor the second derivative of output waveform 10 and exit wait state 110 at a point determined by the second derivative of output waveform 10. In this case, process 90 is effectively doing the analysis done by simulator 52 in the embodiment described above.
Once process 90 reaches the end of the selected interval, the new value of waveform 10 at input 60 of RFA 50 is retrieved 120. The new value of waveform 10 is used along with previously detected values to fit 130 a functional representation to output waveform 10 in the selected interval between the time the new value at input 60 is retrieved 120 and the time the previous value was retrieved 120.
In a preferred embodiment of the present invention, a polynomial fit is employed to represent output waveform 10 in the selected interval. For example, letting sn represent the new value of waveform 10 detected at time tn and sn-1, sn-2, sn-3, . . . represent previous values of waveform 10 detected at times tn-1, tn-2, tn-3, . . . ,respectively, waveform 10 in the selected time interval between tn and tn-1 (the nth interval), may be represented by: ##EQU1## Here, S(τ)n, represents waveform 10 in the nth interval, cmn is the coefficient of the mth power of the time variable, τ, in the polynomial expansion, and M is the order of the polynomial. Each coefficient, cmn, is related to the value of output waveform 10 and its derivatives over the selected interval. The coefficients, cmn, can be computed from the data points and times, {sn, sn-1, . . . } and {tn, tn-1, . . . }, respectively, using any of a variety of well known algorithms.
Once S(τ)n has been fitted 130 from data points {sn, sn-1, . . . } and times {tn, tn-1, . . . } a Fourier integral over the selected interval, tn, tn-1, is computed 140. The Fourier integral for a frequency, f(k)=kω, is given by: ##EQU2## αkm (n) is the analytically integrable integral, 2/T∫τm cos(kωτ) dτ over the interval tn -tn-1, and has the general form: ##EQU3## Here, [m/2] indicates integer division by 2, i.e. [5/2]=2. Thus, the general form of α(n)km may be calculated 140 for the start and endpoints, tn, tn-1 of each selected interval for each frequency of interest. The FIn,k computed 140 for each frequency are added 150 to the Fourier coefficient (FCk) for the frequency which includes the FIp,k calculated for each preceding interval, p, at the frequency, kω. Use of the FIn,k in process 90 eliminates errors due to aliasing as well as errors introduced by approximating the integral of Eq. 4 with a discrete series.
At step 160 it is determined whether the last value of output waveform 10 has been detected. If not, process 90 repeats steps 110-150 for the next interval, n+1. If n is the last interval in waveform 10, process 90 is exited 190.
The resolution with which Fourier coefficients can be computed using the Fourier analyzer of the present invention may be demonstrated by examining the output waveform of a circuit in which harmonic distortion is expected to be minimal. For this purpose, a circuit having a near sinusoidal behavior is selected since the Fourier coefficients of the higher harmonics will be small and therefore difficult to detect.
TABLE 1______________________________________Harmonic SPICE2g6 Spectre Harmonic Balancefundamental 875 mV 1V 1V______________________________________2nd -40.5 dB -98.6 dB -98.5 dB3rd -43.2 dB -116 dB -120 dB4th -24.3 dB -125 dB -169 dB5th -33.3 dB -124 dB -143 dB6th -33.3 dB -125 dB -196 dB7th -24.3 dB -125 dB -165 dBTHD 9.55% .0012% .0012%______________________________________
Referring now to Table 1, there is shown the results of a circuit simulation in which RFA 50 analyzed an output waveform 10 from simulator 52 of a low distortion μa741 operational amplifier in unity gain configuration. Simulator 52, a Spectre simulator, manufactured by Cadence Design Systems, Inc., was driven with a low frequency (1 kHz), low amplitude (1 Volt peak amplitude) driving signal 54 and the first nine harmonics of a 10 ms transient waveform 10 were determined. The second column of Table 1 shows results generated with a conventional discrete Fourier transform (DFT) analyzer provided with a SPICE2g6 simulator. The fourth column of Table 1 shows results generated by harmonic balance, a process that yields highly accurate results for low distortion waveforms. Accordingly, the harmonic balance results serve as a standard in this comparison.
The amplitudes of the fundamental frequency and the second through seventh harmonics were computed for each system. In addition, the total harmonic distortion (THD) is calculated and reported in the last row. As indicated by the harmonic balance results in the third column, the THD for the μa741 operational amplifier exhibits very little harmonic distortion.
A comparison of the second, third, and fourth columns indicates that the Fourier analysis done using the conventional Fourier analyzer of SPICE2g6 is substantially less accurate than the Fourier analysis done using either the RFA of the present invention or the harmonic balance method. For example, the present invention and the harmonic balance method indicate relative amplitudes of -124 dB and -143 dB, respectively, for the fifth harmonic while the DFA method indicates a relative amplitude of -33.3 dB. Similar discrepancies between the DFA based method of column 1 and the methods of columns 3 and 4 are present in the other harmonics and the fundamental.
TABLE 2______________________________________Harmonic SPICE2g6 Spectre Harmonic Balancefundamental 997 mV 1V 1V______________________________________2nd -55.3 dB -98.5 dB -98.5 dB3rd -58.1 dB -120 dB -120 dB4th -53.3 dB -159 dB -169 dB5th -55.9 dB -142 dB -143 dB6th -55.9 dB -164 dB -196 dB7th -53.3 dB -165 dB -165 dBTHD 0.48% 0.0012% 0.0012%______________________________________
The fact that the noise limits in Table 1 are attributable to errors in the waveforms rather than to errors in the Fourier analysis methods is demonstrated with reference to Table 2. Table 2 includes comparable results for the case in which the waveforms were calculated to greater accuracy by setting more stringent limits on the errors tolerated when simulator 52 solves the Kirchoff circuit law. By coincidence, the number of intervals and the placement of the time points defining the intervals was not altered for the method of the present invention. Consequently, the accuracy of the Fourier analysis is substantially unchanged as indicated by the relative size of the amplitudes reported in columns 3 and 4. However, the noise floor does decrease to about -160 dB. The SPICE2g6 results on the other hand show a substantially larger shift as the waveforms are calculated with greater accuracy. However, the accuracy of the Fourier analysis done by the conventional (DFA) method remains substantially less than that of the method of the present invention.
The accuracy with which the Fourier components of a limited number of harmonics can be determined by the method of the present invention is demonstrated by analyzing the output signal of a ΣΔ modulator. Unlike the near sinusoidal output waveform of the μa741 operational amplifier discussed above, the output signal of a ΣΔ modulator is a long sequence of integers. The distortion of the ΣΔ modulator is determined by the value and order of these integers rather than the detailed shape of the waveform. For this reason, the accuracy of the analysis will be independent of the simulator, and an FFT analysis will be accurate as long as the analysis extends over a sufficiently broad frequency range.
Referring now to FIG. 4 there is shown an output signal of a ΣΔ modulator. It can be seen from FIG. 4 that the output signal includes a broad band of frequencies. Consequently, if there are any aliasing problems they will be apparent when the Fourier coefficients of this broad band signal are determined using only some of the many harmonics present in the signal
TABLE 3______________________________________Harmonic Fourier Integral FFTfundamental 1V 1V______________________________________2nd -63.3 dB -63.3 dB3rd -54.3 dB -54.3 dB4th -55.3 dB -55.3 dB5th -51.6 dB -51.6 dB6th -48.9 dB -48.9 dB7th -47.7 dB -47.4 dBTHD 0.905% 1.414%______________________________________
Referring now to Table 3, there are shown Fourier coefficients of the first seven harmonics of the output signal shown in FIG. 4, as computed using the method of the present invention and using a fast Fourier transform (FFT) to compute the discrete Fourier transform. In order to obtain the THD value shown in column 3, the FFT process had to evaluate 512 harmonics. Fortunately, the FFT process is a reasonably efficient means for evaluating discrete Fourier transforms. FFT analyze based on narrower frequency ranges produced substantial error in the calculated Fourier coefficients due to aliasing. Comparable accuracy was obtained for the coefficients calculated with the method of the present invention employing only the first seven harmonics. This is possible because aliasing has been eliminated from the method of the present invention and undetermined harmonics have no impact on the Fourier coefficients of the frequencies of interest.
The FFT method for evaluating discrete Fourier transforms is not used unless the analysis can employ uniform sampling efficiently. For example, consider an RF mixer circuit having an input frequency of 2.7 GHz and an IF output frequency of 500 MHz. To determine the distortion of the mixer, the input signal is modulated at 1 MHz. In this circuit, the IF frequency is the 500th harmonic of the modulation frequency. The mixing of different frequencies creates sharp transitions that would require very small sampling intervals. This effectively precludes the use of uniform sampling and thus FFT. However, the method of the present invention may be applied with no loss of accuracy or efficiency.
TABLE 4______________________________________Harmonic RELTOL = 10-3 RELTOL = 10-6______________________________________496th -81.7 dB -93.1 dB497th -60.0 dB -68.2 dB498th -52.1 dB -53.3 dB499th -6.06 dB -6.05 dB500th 56.2 dB 56.3 dB501st -6.05 dB -6.05 dB502nd -57.7 dB -53.3 dB503rd -63.9 dB -68.4 dB504th -77.4 dB -98.1 dB______________________________________
Referring to Table 4, there is shown a calculation for the amplitudes of the four harmonics on either side of the IF frequency. Since aliasing is not a problem in the method of the present invention, Fourier coefficients need only be computed for the eleven harmonics of interest and the computation can be done efficiently. For example, the minimum interval employed during the analysis using the method of the present invention was about six times smaller than the average interval employed. In order to obtain comparable resolution, the FFT method would have to use the minimum interval throughout the analysis. Consequently, the analysis would take about six times longer.
Referring now to FIG. 5A, there is shown the output of a pulse-width modulator operated at 25 pulses per period, where the width of the output pulses vary sinusoidally with time. Fourier analysis of the output waveform of a pulse-width modulator is difficult to perform efficiently and accurately with conventional DFT analyzers since the output switches from high to low states at arbitrary tintes, whereas the DFT can not resolve transitions that are shorter than the time interval width Δ. This is demonstrated in FIG. 5B, which shows the amplitude of the first through the fifth harmonics as a function of the number of data points analyzed. For example, it requires approximately 104 data points to resolve the first and second harmonics accurately and the third, fourth, and fifth harmonics are still not resolved using more than 105 data points. The number of points necessary to accurately resolve these harmonics increases as the number of pulses per period increases.
TABLE 5______________________________________Harmonic Fourier Integral FFTfundamental 1V 1V______________________________________2nd -48.1 dB -48.0 dB3rd -56.8 dB -56.8 dB4th -93.8 dB -84.6 dB5th 106 dB -88.0 dB6th -138 dB -86.2 dB7th -154 dB -86.2 dB8th -183 dB -87.8 dB9th -201 dB -84.7 dB______________________________________
Referring now to Table 5, there is shown the results of Fourier analyses of a pulse-width modulator using the method of the present invention and using a 64K point FFT. As can be seen from the table, RFA 50 resolves the second through ninth harmonics more accurately than a FFT analysis done using a conventional DFT on 64,000 data points per period. Thus, despite a data base of almost 105 points per pulse, the conventional DFT has failed to resolve the fourth through ninth harmonics. On the other hand, RFA 50 employing process 90 provides high resolution results using 575 data points.
Thus, a ratiometric Fourier analyzer has been presented for analyzing the frequency components of output waveforms with improved accuracy and efficiency. The ratiometric Fourier analyzer of the present invention samples values of the output waveform at time intervals selected in accordance with the properties of the waveform, generates a functional representation of the waveform from the sampled values, and uses the functional representation to analytically evaluate Fourier integrals over the corresponding intervals. The ratiometric Fourier analyzer eliminates errors in signal analysis due to aliasing as well as errors associated with approximating Fourier integrals by discrete Fourier series, and can be used to efficiently determine a small number of Fourier coefficients in broad band signals.
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US6421619 | Oct 2, 1998 | Jul 16, 2002 | International Business Machines Corporation | Data processing system and method included within an oscilloscope for independently testing an input signal |
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US8670969 | Jun 9, 2011 | Mar 11, 2014 | Kenneth Scott Kundert | Circuit simulation system with repetitive algorithmic choices that provides extremely high resolution on clocked and sampled circuits |
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U.S. Classification | 702/77, 324/76.19, 324/608, 324/76.21, 324/76.38 |
International Classification | G01R23/16, G06F17/14 |
Cooperative Classification | G01R23/16, G06F17/141 |
European Classification | G01R23/16, G06F17/14F |
Date | Code | Event | Description |
Oct 28, 1994 | AS | Assignment | Owner name: CADENCE DESIGN SYSTEMS, INC., CALIFORNIA Free format text: ASSIGNMENT OF ASSIGNORS INTEREST;ASSIGNOR:KUNDERT, KENNETH S.;REEL/FRAME:007210/0308 Effective date: 19941024 |
Aug 30, 2000 | FPAY | Fee payment | Year of fee payment: 4 |
Aug 25, 2004 | FPAY | Fee payment | Year of fee payment: 8 |
Aug 19, 2008 | FPAY | Fee payment | Year of fee payment: 12 |


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Carragher: If Liverpool keep Suarez away from Real Madrid he'll be as committed as ever... he won't suffer dip in form like Torres
Jamie Carragher insists Liverpool will not be left the same problems they faced with Fernando Torres should Luis Suarez fail to leave Anfield this summer.
The saga surrounding Suarez's future shows no sign of reaching a swift resolution, as Liverpool have not received an official bid from Real Madrid nor has the player submitted written clarification that he wants out.
It has raised the prospect that Suarez might yet be on Merseyside for the start of the new Barclays Premier League and if that was to happen Carragher is adamant there will not be any worrying or disruptive issues for Brendan Rodgers to deal with.
Talisman: Luis Suarez was Liverpool's top goalscorer last season, which has made Real Madrid take notice
Torres, by contrast, suffered an alarming dip in form after he did not secure a move from Anfield in the summer of 2010, while his attitude was less than impressive at certain times. He eventually joined Chelsea in January 2011 for a record-breaking £50million.
'It's not easy for any club when Real Madrid want one of your players and it's a difficult situation for the club, but if Luis went, it would be top money,' said Carragher, who will start the new campaign as a Sky's new pundit after ending his playing career last month .
'The thing about keeping unhappy players is an issue because we had that experience with Torres; keeping him wasn't the right thing to do. Torres wasn't the same player for about 18 months and downed tools and that's certainly what you don't want.
'But with a character like Luis Suarez, I don't think that would be an issue. If the club were to keep him, I'm sure he would be as committed as ever. He has shown that already –not only on a weekly basis, but on a daily basis. I do believe Suarez is a slightly different character to Torres.
'I don't think Liverpool would ever have the problem (with Suarez) that we had with Torres. If (Suarez) was to be sold, it would be up to the club to make sure the money was spent in the right way, after maybe not doing that after Torres went.'
Suarez's popularity with Liverpool supporters has dipped in the wake of the endless interviews he has given while he has been at The Confederations Cup, while club officials were mystified that he went public with his feelings without giving them any warning.
While Carragher acknowledges the situation has been far from ideal, he does not believe it would be irretrievable for Suarez, if he was to remain on Merseyside.
In demand: Suarez netted a sublime free-kick in the Confederations Cup against Spain
Dip in form: Fernando Torres struggled at Liverpool before joining Chelsea in 2011. This season, Torres found form again for the Blues, scoring 23 times in all competitions under Rafa Benitez
'He has sometimes made the mistake of thinking that what he says over there won' t come back over here,' said Carragher. 'But he is one of the best players in the world and, when Real Madrid come calling, it will turn a player's head.
'They are probably the most famous club in world football, they have the record of winning all those European Cups and, let's not forget, they took Cristiano Ronaldo from Manchester United (in 2009) after United had just been in the Champions League final.
'But the situation is not out of Liverpool's hands because he is under contract (until 2017). He only signed it 12 months ago, so if Liverpool really want to keep him, they can. I don't think it would affect his price too much if he was sold a year later.
'Liverpool would have known they were always going to be in this situation, with other clubs calling for Luis Suarez this summer. That's what happens. They either wait for a bid they think is acceptable or decide to keep him as he is Liverpool's best player and they want to build a team around him.'
Confident: Jamie Carragher is aware of the appeal Real Madrid might have for Luis Suarez
'All eyes will be on them. Swansea away first game will be tough. Then you look at the next two fixtures, the big one for David Moyes is his first home game. You always want to get off to a really good start in front of your supporters but you've got Chelsea and (Jose) Mourinho coming along.
'It isn't going to be easy for (Moyes) and he knows himself if the game at Anfield doesn't go too well there is going to be a lot of talk of Man United at the early start of the season.
'There is a big change at Manchester United, a lot of people are hopefully looking for a change in results because that gives everyone else a chance to be more successful. They are still the team to beat as they are champions.'
Pressure's on: David Moyes takes the reins at Manchester United next season
'If you put me on the spot and ask me right now who will win the league, I would pick Chelsea. Why? Jose Mourinho is coming back and also because they have a very good team with some fantastic players.
'You look at the Premier League last season, and most people would say that Suarez, Bale and Van Persie were the top three players, there's probably no argument about that. But at the same time, (Juan) Mata and (Eden) Hazard were probably four and five.
'This season under a different manager they could easily go on and become THE top players in the league – that's the quality they have. I imagine the players will go the extra yard for Mourinho. He will get the best out of the squad; they have a manager now they will fight for.'
Crucial: Carragher believes Juan Mata (left) and Eden Hazard (right) could step up under Jose Mourinho (below)
'It was strange looking at the fixtures coming out. I was getting as excited seeing Manchester United are facing Chelsea on the second game, as I was that Manchester United are facing Liverpool in the third fixture.
'But that's why I came down this road with Sky, watching different teams, not just being in that bubble of Liverpool Football Club, and concentrating on other sides, players they're bringing in, tactics and formations and things like that.
'I'm sure I will want to pull the boots back on when I'm watching some of the games this season but I've made my decision about wanting to stay in the game. Sky gave me that opportunity.'
Only with Sky Sports can you watch 116 live Barclays Premier League matches, more than ever before, in HD and on mobile and tablet devices
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text: Mischa Barton | Victoria Beckham | Actors | Hot N Spicy | Hot Videos Washington (ANI): Actress Mischa Barton has taken a swipe at Victoria Beckhams style, insisting that the Spice Girl is not a good example of British style. The O.C star has ridiculed Beckhams self proclaimed status as a style guru and believes Brits prefer her own hippy attire. Posh doesnt strike me as particularly stylish, Contactmusic quoted her, as saying. I dont think shes a good example of British style at all. I dont dress for anybody else, and I think the reason people like my style is that I do my own thing, she added.


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Help others choose the best products...
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All alarms and detectors Honeywell X-series can be connected wirelessly using this module EN-XW100. This means that if one detector (carbon monoxide, smoke or fire) alarm is activated and all other connected units will also trigger an alarm. This solution is useful especially in large family houses and larger buildings. Easy to Use - This module is simply mounted on alarms X-series.
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I tried my hand at drawing an ear. Jack Hamm's book helped me to get some feel about the general shape an ear should have (img040). Then I search for a photo of an ear and tried to draw that.
I found that I have the tendency to use to dark lines while sketching. The problem with that is that lines have two purposes. Not only do they mark the edge of the subject, the ear in this case. They're also used to show ridges by representing shades. When you use to dark lines to mark edges it looks like there is a ridge where there should be none.
Yesterday I said that I figured out how shading worked. Today I tried it again.
It's kind of a trick.
I find that I have two modes of looking at a drawing. In the one mode the drawing is flat and darker and lighter areas are just that. Darker and lighter areas.
In the other mode the drawing becomes 3 dimensional and just by looking at the ridges it becomes obvious where shades will be cast and which areas should be darker and which should be lighter.
The trick is to switch from one mode to the other when your drawing needs it. A few days ago I did that by accident and it felt like an epiphany. I didn't even know it was possible.
Today I couldn't get it to work so I had to do it the old fashion way: Work on something else for a few hours and when you return to your drawing you've switched.
Then you can see what you actually drew. You can think about what you should do with your next drawing but you can't actually work on the drawing.
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30 Something Moms
Featured Posts
I now officially have a 3rd Grader and 5th Grader
Big Time Rush stuff of course
Hot Wheels and SkyLanders. Can't believe he will be 11 soon.
First day of school on my Birthday, nothing new there LOL :D
Quoting SallyB_LMT:
I will too. Mine start on the 4th of Sept. I also have 2 younger ones, but they are just doing preschool stuff at home. :)
OP - Your kids are precious! I hope their first day is fantastic!
Quoting CountryGrlAtHrt:
Adorable children!!,I will have a 4TH & 2NCD grader this year...


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Sale £70.00
ChloBo Gold Plated 'Dance Like...' Bangle
This simple yet stunning bangle is the perfect addition for your boho collection this summer, featuring an inscription 'Dance Like Nobody Is Watching'. The fun and stylish bangle is from the fabulouse Sun Dance SS15 collection.
Chlobo is stunning jewellery that looks great from day to night. It looks beautiful worn alone, yet it is irresistibly collectable and has been designed for stacking with other Chlobo pieces. Create your own unique look, and start building your collection.....Chlobo is your story!
The Origin Of Chlobo
Chloe Moss, the founder of Chlobo and Chloboy, spent much of her childhood growing up in the sunshine in Barbados. When Chloe turned 21 she embarked on a journey around the globe looking for creative inspiration and to discover her niche. After visiting many different countries, she eventually ended up on the beautiful island of Bali. This is where her inspiration came from. Within her jewellery, Chloe aims to reflect and encompass the heart and soul that she experienced in Bali.
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Every piece of ChloBo jewellery comes presented in an official ChloBo packaging accompanied with ribbon and a bag. If you require this item to be gift wrapped, please do not hesitate to contact us on email@example.com or call us on 01604 622090.
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I'd Tap That: Dark and delicious Taddy Porter will pair with many delicious food items
Glassware: Taddy Porter is a true gem in the English porter category and should be experienced to its fullest to truly appreciate this beer. The aroma is both rich and decadent and glassware that helps capture that aroma is a must. A stemmed porter glass is certainly an option, but not a common sight at many bars. However, an oversized wine glass or snifter are viable options and allow for a great experience with this world class beer.
Description: Taddy Porter pours a dark midnight black with creamy brown head that leaves wisps of lacing on the glass. The aroma is very decadent with notes of chocolate, dried red fruits, cream, coffee and roasted malt, all in perfect balance. The taste follows the nose but is even more expansive as it slowly warms up. Dark chocolate is the first flavor to rush across the palate with notes of coffee intertwined and backing of sweetness that comes across as dried red fruits and cream with hints of bitterness from earthy hops and bitter chocolate. The flavors linger long on the palate and that is just what you want! The medium body and carbonation are impactful in giving this beer a smooth and creamy mouthfeel that just adds to the decadent experience. Many drinkers claim to not enjoy darker beers because they are too roasty or bitter, but Taddy Porter proves that dark beers are far from just one-flavor beers and this is a must try for all beer lovers!
Food Pairing: While the description of the beer may make it sound like it is a great dessert beer there is a better option with this classic English porter — seafood! If you have ever traveled to the United Kingdom you may know the joy of eating fresh seafood by the shore and enjoying a pint of porter with it. The combination of salt and sweet is absolutely perfect. For a small slice of this heaven on Earth, try pairing Taddy Porter with fresh oysters. The heavy salt flavors from the oysters will melt into the indulgent chocolate flavors of the beer and act as the perfect counterpoint for the beer. Many from the shellfish category make for the best pairing with Taddy Porter, so try them all. However, if you are not a seafood fan fear not, Taddy Porter is also a dream pairing with steak. Try this beer with your next porterhouse steak and you will wonder why you haven't try this combination previously. It should also be noted that Taddy Porter is a natural match with dessert, specifically chocolate based desserts.
The Final Word: In this current craft beer market, where breweries and beers come in and out of fashion by the week, sometimes the tried and true beers are forgotten by many. This is an unfortunate fact especially with a beer as phenomenal as Taddy Porter being widely available. This English porter helped lay the groundwork for many of today's craft brewers. The rich flavors and aromas are a showcase of how great a well brewed porter could and should be and opened the eyes of many brewers to great beer. If you are one of the guilty who have seen this beer on shelves but have not tried it yet, do yourself a favor and buy some now. All fans of porters, stouts or good beer must check this beer off their beer bucket list.
Derek Warren is a beer fanatic, avid homebrewer and beer historian. Derek can be heard weekly on the Beer Geeks Radio Hour at noon on Sundays on WILK 103.1 FM with past episodes available on iTunes.
Brewery: Samuel Smith Old Brewery
Beer: Taddy Porter
Style: English Porter
Rating: WWWWW
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Item description for Miracle Maker: The Selected Poems of Fadhil Al-Azzawi (Lannan Translations Selections.) by Fadil Azzawi, Khaled Mattawa & Khaled Mattawa...This collection features poems from Al-Azzawi's six previous Arabic poetry collections and many new poems. Springing from classical Arabic poetry, his poems speak to political exile, -cultural marginalization, and Middle Eastern and Western histories and mythologies. Al-Azzawi employs -humor, melancholy and tenderness to celebrate new worlds of possibility. Fadhil Al-Azzawi was born in 1940 in Kirkuk, Iraq. By the time he was -fifteen, he was publishing poems in the leading Arab literary magazines in Beirut and Baghdad. Al-Azzawi -currently lives in London. Khaled Mattawa (Translator) is the author of a -collection of poetry, Ismailia Eclipse, and the translator of two books of contemporary Arabic poetry, Hatif Janabi's Questions and Their Retinue and Saddi Youssef's Without an Alphabet, Without a Face. Promise Angels is dedicated to bringing you great books at great prices. Whether you read for entertainment, to learn, or for literacy - you will find what you want at promiseangels.com! Item Specifications...
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Hotel Gault
Select your stay dates to check availability at Hotel Gault
Hotel Gault
About the Hotel
Property Location
With a stay at Hotel Gault in Montreal (Old Montreal), you'll be minutes from World Trade Center Montreal and Notre Dame Basilica. This 4-star hotel is within close proximity of Palais des congres de Montreal and Centaur Theatre.
Make yourself at home in one of the 30 air-conditioned rooms featuring iPod docking stations and minibars. Wired and wireless Internet access is complimentary, and flat-screen televisions with cable programming provide entertainment. Bathrooms have hair dryers and bathrobes. Conveniences include laptop-compatible safes and coffee/tea makers, as well as phones with free local calls.
Take advantage of recreation opportunities such as a 24-hour fitness center, or other amenities including complimentary wireless Internet access and concierge services. Additional amenities at this hotel include babysitting/childcare (surcharge) and a fireplace in the lobby.
Satisfy your appetite at the hotel's restaurant, which serves breakfast, lunch, and brunch. Dining is also available at a coffee shop/café, and 24-hour room service is provided. Quench your thirst with your favorite drink at a bar/lounge.
Business, Other Amenities
Featured amenities include complimentary high-speed (wired) Internet access, a computer station, and dry cleaning/laundry services.
Hotel Facilities
- Luggage storage
- Total number of rooms - 30
- Babysitting or childcare (surcharge)
- 24-hour fitness facilities
- Elevator/lift
- Free WiFi
- Coffee shop or café
- Smoke-free property
- Number of floors - 5
- Fireplace in lobby
- Computer station
- Dry cleaning/laundry service
- 24-hour front desk
- Bar/lounge
- Accessible bathroom
- Valet parking (surcharge)
- In-room accessibility
- Babysitting or childcare
- Free wired high-speed Internet
- Concierge services
- Breakfast available (surcharge)
- Meeting rooms 2
- Restaurant
- Library
- Tours/ticket assistance
Room Facilities
- Air conditioning
- Rollaway/extra beds (surcharge)
- Phone
- Cable TV service
- Room service (24 hours)
- In-room climate control (air conditioning)
- Free wired high-speed Internet
- Coffee/tea maker
- Connecting/adjoining rooms available
- Premium bedding
- iPod docking station
- Free local calls
- In-room safe (laptop compatible)
- Hair dryer
- Bathrobes
- Minibar
- Blackout drapes/curtains
- DVD player
- Turndown service
- Flat-panel TV
- Free bottled water
- Iron/ironing board
- Free WiFi
- Hypo-allergenic bedding available
- Free cribs/infant beds
Hotel Policy
Know Before You Go
- The property has connecting/adjoining rooms, which are subject to availability and can be requested by contacting the property using the number on the booking confirmation.
The following fees and deposits are charged by the property at time of service, check-in, or check-out.
- Breakfast fee: between CAD 18 and CAD 25 per person (approximately)
- Valet parking fee: CAD 35 per night
- Pet fee: CAD 60 per pet, per night
- Rollaway bed fee: CAD 85 per night
The above list may not be comprehensive. Fees and deposits may not include tax and are subject to change.
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Mitt Romney, a Republican businessman who was in charge of the Salt Lake City Winter Olympics, was elected governor of Massachusetts today, defeating Shannon O'Brien, the Democratic state treasurer.
With 66 percent of the precincts counted, Mr. Romney had won 52 percent of the votes to 43 percent for Ms. O'Brien, 763,153 votes to 640,423.
Mr. Romney, 55, won after the most expensive political race in Massachusetts history in which the two candidates had been in a virtual dead heat in the polls for the last week.
Mr. Romney emphasized his business experience as the leader of Bain Capital, an investment firm, and his success in the 2002 Winter Olympics, appealing to voters as a political outsider who could fix a huge state budget shortfall and bring jobs to Massachusetts.
''We took on an entrenched machine and we won,'' Mr. Romney said in his acceptance speech.
In winning, Mr. Romney overcame two handicaps. He ran as a Republican in a largely Democratic state, and he is a Mormon in a heavily Roman Catholic state.
Mr. Romney's victory was also a personal vindication after he lost a race for the United States Senate in 1994 to Senator Edward M. Kennedy. Mr. Romney's father, George Romney, was governor of Michigan who made an unsuccessful bid for the Republican presidential nomination in 1968.
Some Democrats initially expressed skepticism that Mr. Romney would serve out his term as governor of Massachusetts and was simply using the election as a steppingstone to become Republican candidate for vice president or even president. But these doubts did not seem to influence voters, and Mr. Romney carried even such urban Democratic strongholds as Brockton and Quincy.
Mr. Romney will replace Jane M. Swift, the acting governor, a widely unpopular Republican who inherited the job when Gov. Paul Cellucci resigned after President Bush nominated him to be United State ambassador to Canada. Ms. Swift, who had been lieutenant governor, had been expected to run as the Republican candidate for governor this fall until Mr. Romney, sensing her weakness, returned from Utah after the Olympics and drove her out of the race.
Mr. Romney will face a severe state budget crisis, with tax revenue taking the biggest plunge in 50 years, said Michael J. Widmer, president of the Massachusetts Taxpayers Foundation, a nonpartisan research group backed by businesses.
After a decade of rapid economic growth, Massachusetts legislators had embarked on ambitious programs combining tax cuts with increased spending for education and health care. But with capital gains and income tax revenue in free fall, the new governor's main task will be to slash state spending and try to balance the budget.
In television advertisements, Mr. Romney said his business experience would help him balance the budget and cut state taxes while attracting new businesses and jobs. Ignoring the fact that Republicans have been governor of Massachusetts for the last 12 years, Mr. Romney also promised to ''clean up Beacon Hill,'' the location of the statehouse.
Ms. O'Brien, the daughter of a political family from western Massachusetts, has been a state legislator as well as state treasurer and has close relations with the Democrats who control the Legislature. In her campaign, Ms. O'Brien was strongly supported by traditional Democratic groups, including labor unions and public school teachers.
But she was hurt by Mr. Romney's attacks on her husband, who is a lobbyist, and she lost votes to the Green Party candidate, Jill Stein.
Continue reading the main story


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Simone Lopez
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Plumber's union.<quoted text>
but we are both male and female. what union or we designed for?
Judge overturns California's ban on same-sex marriage
There are 201878 comments on the www.cnn.com story from Aug 4, 2010, titled Judge overturns California's ban on same-sex marriage. In it, www.cnn.com reports that:
A federal judge in California has knocked down the state's voter-approved ban on same-sex marriage, ruling Wednesday that the state's controversial Proposition 8 violates the U.S. Constitution.
Join the discussion below, or Read more at www.cnn.com.
"Vita e' Bella." Since: May 12 14,378 Location hidden |
Feb 7, 2013
Since: Mar 09 2,754 Location hidden |
Feb 7, 2013
LIke forced marriages in prison? Yeah, we've already seen just how many of those have occured in Canada. Perhaps you need to rethink, with some intelligence for a change, what those probable consequences might be before banging on about them. |
Feb 7, 2013
Oh no, I am on the right side of history, same sex marriage is legal now, in a growing number of states and countries. You can cry and whine and pine for the "good old days" all you want, but it isnt going to do you any good, same sex marriage will continue to become legal in more and more states |
"Reality bites" Since: Dec 11 3,269 Location hidden |
Feb 7, 2013
1) the boy scouts are a club somewhat, open for all boys to join, unless of course if you are gay. 2) Who said you have to be married in a church? BTW there are a few churches that will preform a traditional marriage ceremony. |
Feb 7, 2013
The topic of this blog is:Judge overturns ban on same sex marriage in California.
Everything else is off topic. Of course homosexuals should have equal rights to legal marriage. Everything else is off topic. I have seen both homosexual and heterosexuals display lust, and I have seem both homosexuals and heterosexuals display love. Only a couple should decide if they are in love and want to have the legal right to be married. |
Feb 7, 2013
Not one of those arguments were against it, just pointing out some facts. I am not against it, I just dont care, as I know nothing is going to happen with it for a long long time. Immoral religious degenerates have made absolutely certain of that. If you think otherwise then build your case, put it on a ballot, have a vote, send it to the Supreme Court, but dont be asking me for a donation because I could not care less. I already know the outcome of your efforts. |
Feb 7, 2013
Wrong, a church is a private little club, they can refuse to marry people with blue eyes, they can refuse to marry someone because they are a republican. This is not about some church or other, this is about legal marriage, which requires no church at all, no mention of any "holy books" or beliefs and can take place in your kitchen if you want it to with someone with the right paperwork and authorized by the state to do so.( I know, I have been to one of those ) Also, who is defending the rights of churches that WANT to preform same sex marriages and are being denied the right to do so? There are tens of thousands of those as well. |
Feb 7, 2013
Wow! Imagine if someone posted similar hate, ignorance and bigotry against gay marriage. |
Feb 7, 2013
The shoe is on the other foot,now the hunter's have become the hunted?
Feb 7, 2013
But it's completely acceptable to violate the constitution and mandate government healthcare.
I see how this works... |
Feb 7, 2013
What hate, I am explaining that any church can decide not to marry anyone for any reason they want, no matter how silly the reason, as their rules only apply to their little church. I am defending a churches right to specifically deny doing a marriage regardless of the legality of same sex marriage. learn to read |
Feb 7, 2013
Government healthcare? What have you got against Medicare? |
Feb 7, 2013
sorry wrong post I replied to are you complaining about my hatred of Immoral religious child molesters? Too bad |
Feb 7, 2013
A police officer has been demoted for sending sexually-explicit video to her boyfriend.
Lopez herself is now reportedly considering a lawsuit against the city. Her lawyer explained that her case would be based on "constitutional issues over lawful off-duty behavior and violation of privacy." |
Feb 7, 2013
Smoke out
Feb 7, 2013
Thank you Jesus
Feb 7, 2013
No I am pointing out bigotry and ignorance in condemning a whole group due to the actions of a few. There are some bad homosexuals too. Does that mean we should label all homosexuals bad? Of course not. But that is exactly what you are doing with polygamists. Hope that helps. |
Feb 7, 2013
This hate: "Immoral religious degenerates" |
Feb 7, 2013
Hey it is black history month so I get to slap a white peron first my cracker husband (smile) but he will just enjoy it Hey frank why is your cousin police officer Willie shooting up people(smile)
Feb 7, 2013
Yeah, people that force children to have sex with older men, the ones in the news you see all the time, and anyone that disagrees that they are Religious immoral degenerates is also an immoral degenerate. |
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Prisoner Gocha Archaia Died because of Negligence
On February 22, prisoner Gocha Archaia, 41, died in the Gldani Jail Hospital # 18. His health conditions were extremely grave. Although he suffered from several acute diseases, he was not released from imprisonment before death.
Gocha Archaia took medical treatment for the following diseases: lung tuberculosis in the phase of infiltration; AIDs C3 Category with consummation syndrome; chronic diarrhea; chronic C virus hepatitis, chronic phringit. On February 10, 2010, based on the decision of the medical consultation group, the sick person involved the program for anti-tuberculosis treatment.
Head of the Legal Aid Center at the Human Rights Center Nino Andriashvili was attorney of the late prisoner. She said Gocha Archaia willfully stopped anti-AIDs therapy because the medicines had side-effects like: weakness, dizziness, pain in limbs and difficulties of movement. The Scientific-Practical Center for the Infection Pathology AIDs and Clinical Immunology confirmed the information.
The prisoner was registered at the Scientific-Practical Center since November 24, 2005. He took last tests on March 16, 2010 and they diagnosed: AIV Infection/AIDs, C3 Category; active tuberculosis infection, chronic C virus hepatitis.
In accordance to the Article 13 Part III of the resolution # 72/n of the Ministry of Labor, Healthcare and Social Welfare, convicted person can be released from imprisonment based on the AIV Infection AIDs with consummation syndrome.
On September 22, 2011 the lawyer of the Human Rights Center Nino Andriashvili petitioned to the joint commission of the Ministry of Corrections and Legal Aid and Ministry of Labor, Healthcare and Social Welfare of Georgia to study health conditions of Gocha Archaia and release him from imprisonment early in time. The Commission had to make decision within one month but they did not study the case yet, despite the petition of the lawyer.
During his last meeting with the lawyer, the convicted requested permission to spend his last days with his children and wife.
The Human Rights Center is extremely astonished with the negligence and inattention of the joint commission of the Ministry of Correction and Legal Aid and Ministry of Labor, Healthcare and Social Welfare towards the prisoners. The Center hopes Gocha Archaia will be the last prisoner who dies in prison and in future the Commission will implement its responsibilities under the law – to timely study similar cases and release adequate decisions.
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text:
Computer Games & Entertainment
Entry requirements
Upper second class undergraduate degree in computing, engineering or mathematical sciences, and an interest in - and capability for - working in interdisciplinary contexts. You will be required to demonstrate sufficient proficiency at programming in a major language. Applicants with professional experience will also be considered.
Months of entry
Course content
Our groundbreaking MSc has been developed in response to a pressing need to offer a high quality postgraduate programme serving the industries of computer games and entertainment, with an emphasis on programming, maths and graphics, business, IP, entrepreneurship, team management, 3D animation, AI and physics in games. The programme is delivered by a mix of professionals from the industry and from the research world.
The computer games and entertainment business is a fast growing multi-billion pound worldwide business, with games platforms ranging from Playstation 3, Xbox 360, Nintendo Wii, mobile and handhelds, PC-based, and massively multiplayer online games (MMOG) involving tens of thousands of people.
With ongoing strong demand for graduate computer games programmers from the UK and abroad, this MSc will produce graduates who are well positioned to get a job in this exciting worldwide industry. Potential employers include EA, Ubisoft, THQ Sony, Activision, Microsoft, and many more.
In a wider sense, the influence of computer games programming is spreading to other industries outside games, as seen in products such as Second Life, Habbo Hotel and Bebo, or as seen in other entertainment industries such as special effects for television, videos and movies. Computer games are starting to fundamentally change the way people interact with computerised systems.
Qualification and course duration
Course contact details
- Name
- Course Enquiries
- email@example.com
- Phone
- +44 (0)20 7078 5300


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Thread Tools | Search this Thread |
10th September 2011, 12:38 PM | #1 |
diyAudio Member
Join Date: May 2007
Subwoofer DIY
I enclose the pictures of a subwoofer amp module I completed.Here are the details
Out put power- 25 watts rms max AC input- 18-0-18 2A Input- Both low level and line level Subwoofer filter type- Sallen &Key 18db/octave Crossover frequency 200 cycles Power amp IC LM1875 I can furnish any other information if requested
deevee |
12th September 2011, 01:30 AM | #2 |
diyAudio Member
Join Date: Jan 2011
25 rms for a subwoofer amp? You sure you didn't mean tweeter amp? jk but what subs are you driving with this??
16th September 2011, 01:51 AM | #3 |
diyAudio Member
Join Date: May 2007
Sub woofer DIY
Thanks for your query
I wanted to add bass to a pair of computer speakers. I drafted the circuit,designed the PCB in Eagle,got the PCB manufactured by Futurlec in China and assembled the module.I am feeding this into a 13 liter bass reflex ported cabinet made by me in 3/4" MDF.The speaker is a 6 1/2 inch Dayton woofer DC160s-4 from PartsExpress.They sound great. Yes you are right in that they dont deliver heart thumping bass but more than serve the purpose for which they were made. I have one extra PCB for the module.If anybody is interested ,let me know.
deevee |
22nd September 2011, 09:17 PM | #4 | |
diyAudio Member
Join Date: Jul 2005
Location: D-55629 Schwarzerden
Ultimate Solution for an User with already present "InWall" Subwoofer:ESL or dynamicL 10 watts rms is much more than enough !!! For security reasons (to prevent hearing damage and glass breakage) you should not use amplifiers with higher output power. The only reason for the use of six drivers is to achieve a homogeneous bass (without maximas and zeros) throughout the room. Last edited by tiefbassuebertr; 22nd September 2011 at 09:21 PM. |
4th October 2011, 03:34 PM | #5 |
diyAudio Member
Join Date: May 2007
Subwoofer DIY
I want to also publish an excerpt from the Philips Eindhoven book on power amplifiers published way back but which still holds. I have copied it verbatim with no embellishments from my side.
"Because of the large number of variables affecting room acoustics it is only possible to approximate the power requirements for high fidelity reproduction. Realistic results can be obtained using the following simplified method of determination. The acoustic power at Threshold of hearing at 100Hz can be taken to be P (threshold) =1X10 -14 V/t watts where V is the volume of room in cubic meters and T is the reverberation time in Seconds. For small rooms up to say 100m3 , T has a value of 0.5 seconds. Assuming that the listening room measures 5 meters long 4 meters wide and 3meters high the volume will be 60 m3.For max of 90 db above the threshold mentioned above the acoustic power will be P max=(4x10-14x60x109) / .5 =4.8mw Taking the efficiency of the speaker system to be 1% the electrical power input would be 100x4.8mw=0.48 w The ear is less sensitive to bass at low volumes and the relation is depicted in the Fletcher Munson curves It can be seen from them that at 90 db the curves are substantially flat over the bass region and so the relatively low electrical power of .48 w will be adequate to reproduce the signal at a signal level of 90 db over the whole band. However if we examine the curve for 30 cycles and considering that the low listening level is in the range of 50 db we can see that the low frequencies have to be bumped up by 20 db or so. This is usually provided in the amplifier by a tone control with 20db boost/cut usually of the baxandall design. Hence the power requirement comes to .48wx100=48W. In calculating the above power requirement we have not considered speaker positioning.Usualy subwoofers are heavy and are placed on the ground against a wall or corner. Because of the reflecting nature of the walls the apparent power is amplified by 8 times for a corner and 4 times against a wall. Also the efficiency of 1% used in the above calculation is for a closed box design. Usually all subwoofer enclosures are of the bass reflex design with efficiencies typically 2.5 to 3 times the closed box efficiency over the sub woofer frequencies up to 200 cycles. In summary even for a fairly large room a power of 50 watts is more than sufficient for the sub woofer. A 25w rms subwoofer is more than sufficient for a moderate size room unless you want to develop hearing and heart issues.
deevee |
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text:
--- Begin Message ---
- To: Adam Di Carlo <email@example.com>, email@example.com, firstname.lastname@example.com
- Subject: Re: Comments on Debian packages and installation
- From: Joseph Carter <firstname.lastname@example.com>
- Date: Wed, 30 Dec 1998 13:55:39 -0800
- Message-id: <firstname.lastname@example.com>
- References: <firstname.lastname@example.com> <email@example.com> <email@example.com> <firstname.lastname@example.com> <firstname.lastname@example.com> <email@example.com> <firstname.lastname@example.com> <email@example.com> <email@example.com> <firstname.lastname@example.com>
On Wed, Dec 30, 1998 at 12:16:42PM -0800, Joey Hess wrote: > > As you may know, no package in the main Debian distribution may > > 'depend' or 'recommend' a non-free package. The 'suggests' > > relationship, which is only intepreted by dselect, needs to have it's > > GUI mechanics tuned so that relationships with non-free packages are > > *presented* without actually causing users to worry that they need > > that package. I think that can be done pretty simply with some > > verbage in dselect. > > Everyone (except maybe Joseph Carter) seemed to ignore/not understand my > earlier message about this, so I'll say it again: > > All we need to do is change dselect so if there is a Suggests: that points > to a package that is not in the available file, dselect does not show it to > the user. This will make users who do not have non-free selected at all not > see the suggests, and users who do chose to have non-free selected see them. > > (Do you have a bug number yet for this bug report I can send this message to?) Actually, it'd do to have it say "Ignoring suggestion for <package>" Of course I am certain someone will ask "why did it ignore the suggestion?" and we can either point them at something resembling docs or tell them it's because the package isn't available and it's only suggested anyway so it's not a big deal. Or something like that anyway. -- "In the beginning the Universe was created. This has made a lot of people very angry and been widely regarded as a bad move." -Douglas Adams
--- End Message ---


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NFL VP of officiating acknowledges blown call in Cowboys-Packers game Mike Pereira, NFL VP of officiating, admitted to a blown call in the Cowboys-Packers game. [url=http://sports.espn.go.com/dallas/nfl/news/story?id=4658671&campaign=rss&source=NFLHeadlines]More...[/url] |
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