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ADVANCES IN AUDIO SIGNAL ENHANCEMENT AND STRINGED INSTRUMENT EMULATION USING REAL-TIME DSP

A new generation of digital signal processors combined with flexible real-time software is facilitating progress in acoustic and musical technologies in several key areas, three of which are considered here: first, how musical or audio-bandwidth signals may be modified, enhanced or deliberately degraded; second, how sounds produced by musical instruments can be decomposed with extreme precision into distinct frequency and phase groupings, fostering a greater understanding of the psychoacoustic parameters that determine how we perceive factors such as musical quality; finally, how the frequency responses of stringed instruments may be exploited, by employing these fast real-time processors in the development of new "digital-acoustic" instruments with exceptional acoustic fidelity. Advances in these subjects have occurred predominantly as a result of real-time digital signal processing (DSP). A simple, linear, arbitrary frequency and phase response filter, with a real-time spectral resolution of over one part in one thousand is impossible to design using analogue components, yet forms the basis of the instrument body impulse response. Although it might be argued that real-time DSP fundamentally does not alter our understanding of the physical principles underpinning the production of sound from acoustic instruments, it is also the case that in recent times, the quantitative improvement in speed of these devices has made possible the execution of tests previously considered "thought experiments". In turn, these may yet provide new and qualitatively different insights into psychoacoustic mechanisms. INTRODUCTION Real-time signal processing based on both general purpose microprocessors and fast digital signal processors (DSPs) is a technique that emerged over twenty years ago, and is now widely considered one of the fastest growing application areas in the field of digital technology. Applications include biomedical signal analysis, image analysis, image coding and decoding, and audio signal enhancement [1-4]. Typically, the analogue waveform is first digitized by an analogue to digital converter (ADC), and the binary values are transmitted to a DSP device that performs a real-time convolution operation in discrete space using either a finite impulse response (FIR) or infinite impulse response (IIR) algorithm. The processed data are then sent to a digital to analogue converter (DAC) that outputs a filtered analogue signal. In order to meet the requirements of the Sampling Theorem with respect to the incoming waveform, and to eliminate quantization noise in the processed signal, an anti-aliasing filter is included before the ADC and similarly, a reconstruction filter is included after the DAC. Filters constructed using DSP technology offer many advantages over traditional analogue methods. They are inherently flexible, since changing the characteristics of the filter merely involves changing the program code or filter coefficients; with an analogue filter, physical reconstruction is required. Furthermore, they are immune to the effects of ageing and environmental conditions, since the filtering process is dependent on numerical calculations, not mechanical characteristics of the components. This makes them particularly suited for very low frequency signals. For the same reason, the performance of digital filters can be specified with extreme precision, in contrast to analogue filters where a 5% figure is considered excellent. BASIC DSP FILTER THEORY The (linear) process of filtering in time t is encapsulated in the convolution integral τ τ τ d t x h t y ) ( ) ( ) ( − = ∫ ∞