Amplitude-shift keying

From Wikipedia, the free encyclopedia
  (Redirected from Amplitude Shift Keying)
Jump to navigation Jump to search

Amplitude-shift keying (ASK) is a form of amplitude modulation that represents digital data as variations in the amplitude of a carrier wave. In an ASK system, a symbol, representing one or more bits, is sent by transmitting a fixed-amplitude carrier wave at a fixed frequency for a specific time duration. For example, if each symbol represents a single bit, then the carrier signal will be transmitted when the input value is 1, but will not be transmitted when the input value is 0.

Any digital modulation scheme uses a finite number of distinct signals to represent digital data. ASK uses a finite number of amplitudes, each assigned a unique pattern of binary digits. Usually, each amplitude encodes an equal number of bits. Each pattern of bits forms the symbol that is represented by the particular amplitude. The demodulator, which is designed specifically for the symbol-set used by the modulator, determines the amplitude of the received signal and maps it back to the symbol it represents, thus recovering the original data. Frequency and phase of the carrier are kept constant.


The simplest and most common form of ASK operates as a switch, using the presence of a carrier wave to indicate a binary one and its absence to indicate a binary zero. This type of modulation is called on-off keying (OOK), and is used at radio frequencies to transmit Morse code (referred to as continuous wave operation),


ASK diagram


  • ht(f) is the carrier signal for the transmission
  • hc(f) is the impulse response of the channel
  • n(t) is the noise introduced by the channel
  • hr(f) is the filter at the receiver
  • L is the number of levels that are used for transmission
  • Ts is the time between the generation of two symbols

Different symbols are represented with different voltages. If the maximum allowed value for the voltage is A, then all the possible values are in the range [−A, A] and they are given by:

the difference between one voltage and the other is:




where we use the notation:


In this relationship, the second term represents the symbol to be extracted. The others are unwanted: the first one is the effect of noise, the third one is due to the intersymbol interference.


the transmission will be affected only by noise.

Probability of error[edit]

The probability density function of having an error of a given size can be modelled by a Gaussian function; the mean value will be the relative sent value, and its variance will be given by:


The probability of making an error is given by:

where, for example, is the conditional probability of making an error given that a symbol v0 has been sent and is the probability of sending a symbol v0.



Ask dia calc prob.png

The probability of making an error after a single symbol has been sent is the area of the Gaussian function falling under the functions for the other symbols. It is shown in cyan for just one of them. If we call the area under one side of the Gaussian, the sum of all the areas will be: . The total probability of making an error can be expressed in the form:

We now have to calculate the value of . In order to do that, we can move the origin of the reference wherever we want: the area below the function will not change. We are in a situation like the one shown in the following picture:

Ask dia calc prob 2.png




This relationship is valid when there is no intersymbol interference, i.e. is a Nyquist function.

See also[edit]

External links[edit]