Convolution and sound synthesis

Abstract

If the source signal and the system’s transfer function or impulse response are obtained separately, the resulting output signal can be calculated by convolution (Eq. (7.3)). The convolution can be processed in various ways, either directly in the time domain by using FIR filters or by using FFT convolution. In the latter case, however, it should be kept in mind that FFT requires fixed block lengths and is related to periodic signals. Time windows might be required for reducing artefacts from discontinuities. The same holds for framewise convolution in slowly time-variant systems. Also, the technique of convolution or “filtering” (IIR, FIR) is valid for LTI systems exclusively. For time-varying systems, the excitation signal must be processed in frames representing pieces of approximate time invariance. In this case, filters might be adapted while processing and fading must be used to move from frame to frame.