What is a Filter?

Any medium through which the music signal passes, whatever its form, can be regarded as a filter. However, we do not usually think of something as a filter unless it can modify the sound in some way. For example, speaker wire is not considered a filter, but the speaker is (unfortunately). The different vowel sounds in speech are produced primarily by changing the shape of the mouth cavity, which changes the resonances and hence the filtering characteristics of the vocal tract. The tone control circuit in an ordinary car radio is a filter, as are the bass, midrange, and treble boosts in a stereo preamplifier. Graphic equalizers, reverberators, echo devices, phase shifters, and speaker crossover networks are further examples of useful filters in audio. There are also examples of undesirable filtering, such as the uneven reinforcement of certain frequencies in a room with ``bad acoustics.'' A well-known signal processing wizard is said to have remarked, ``When you think about it, everything is a filter.''

A digital filter is just a filter that operates on digital signals, such as sound represented inside a computer. It is a computation which takes one sequence of numbers (the input signal) and produces a new sequence of numbers (the filtered output signal). The filters mentioned in the previous paragraph are not digital only because they operate on signals that are not digital. It is important to realize that a digital filter can do anything that a real-world filter can do. That is, all the filters alluded to above can be simulated to an arbitrary degree of precision digitally. Thus, a digital filter is only a formula for going from one digital signal to another. It may exist as an equation on paper, as a small loop in a computer subroutine, or as a handful of integrated circuit chips properly interconnected.