The term filter can have a large number of different meanings. In general it can be seen as a way to select certain elements with desired properties from a larger set. Let us focus on the particular field of digital audio effects and consider a signal in the frequency domain. The signal can be seen as a set of partials having different frequencies and amplitudes. The filter will perform a selection of the partials according to the frequencies that we want to reject, retain or emphasize. In other words: the filter will modify the amplitude of the partials according to their frequency. Once implemented, it will turn out that this filter is a linear transformation. As an extension, linear transformations can be said to be filters. According to this new definition of a filter, any linear operation could be said to be a filter, but this would go far beyond the scope of digital audio effects. It is possible to demonstrate what a filter is by using one's voice and vocal tract. Utter a vowel, a, for example, at a fixed pitch and then utter other vowels at the same pitch. By doing that we do not modify our vocal cords, but we modify the volume and the interconnection pattern of our vocal tract. The vocal cords produce a signal with a fixed harmonic spectrum, whereas the cavities act as acoustic filters to enhance some portions of the spectrum. We have described filters in the frequency domain here because it is the usual way to consider them, but they also have an effect in the time domain. After introducing a filter classification for basic filter types in the frequency domain, we will review typical implementation methods.
Beyond their effects in the frequency domain, filters can also be considered in the time domain leading to a family of delay-based audio effects such as those which can be experienced in acoustical spaces. A sound wave reflected by a wall will be superimposed on the sound wave at the source. If the wall is far away, such as a cliff, we will hear an echo. If the wall is close to us, we will notice the reflections through a modification of the sound color. Repeated reflections can appear between parallel boundaries. In a room, such reflections will be called flatter echo. The distance between the boundaries determines the delay that is imposed on each reflected sound wave. In a cylinder, successive reflections will develop at both ends. If the cylinder is long, we will hear an iterative pattern, whereas if the cylinder is short, we will hear a pitched tone. Equivalents of these acoustical phenomena have been implemented as signal processing units. In the case of a time-varying delay the direct physical correspondence can be a relative movement between sound source and listener imposing a frequency shift on the perceived signal, which is commonly referred to as the “Doppler effect.”