Allpass Filters

The allpass filter is an important building block for digital audio signal processing systems. It is called ``allpass'' because all frequencies are ``passed'' in the same sense as in ``lowpass'', ``highpass'', and ``bandpass'' filters. In other words, the amplitude response of an allpass filter is 1 at each frequency, while the phase response (which determines the delay versus frequency) can be arbitrary.

In practice, a filter is often said to be allpass if the amplitude response is any nonzero constant. However, in this book, the term ``allpass'' refers to unity gain at each frequency.

In this section, we will first make an allpass filter by cascading a feedback comb-filter with a feedforward comb-filter. This structure, known as the Schroeder allpass comb filter, or simply the Schroeder allpass section, is used extensively in the fields of artificial reverberation and digital audio effects. Next we will look at creating allpass filters by nesting them; allpass filters are nested by replacing delay elements (which are allpass filters themselves) with arbitrary allpass filters. Finally, we will consider the general case, and characterize the set of all single-input, single-output allpass filters. The general case, including multi-input, multi-output (MIMO) allpass filters, is treated in [452, Appendix D].