Filtering is still one of the most commonly used effect tools for sound recording and production. Nevertheless, its successful application is heavily dependent on the specialized skills of the operator. In this chapter we have described basic filter algorithms for time-domain audio processing. These algorithms perform the filtering operations by the computation of difference equations. The coefficients for the difference equations are given for several filter functions such as lowpass, highpass, bandpass, shelving and peak filters. Simple design formulas for various equalizers lead to efficient implementations for time-varying filter applications.
Delays are used in audio processing to solve several practical problems, for example delay compensation for sound reinforcement systems, and as basic building blocks for delay-based audio effects, artificial reverberation and physical models for instrument simulation. The variety of applications of delays to spatial effects will be presented in Chapter 5.
This brief introduction has described some of the basic delay structures, which should enable the reader to implement and experiment with delay algorithms on their own. We have further pointed out that a comb-filter effect emerges if a delayed copy of the signal is mixed with the nondelayed signal. Thus we established an intuitive link between delays and filters, which is especially helpful in understanding their time-varying application. We have focused on a small set of important delay-based effects such as echo, vibrato, flanger and chorus and introduced the principle of multiband effects. These basic building blocks may serve as a source of ideas for designing new digital audio effects.