Audio FIR Filters

FIR filters shorter than the ear's ``integration time'' can generally be characterized by their magnitude frequency response (no perceivable ``delay effects''). The nominal ``integration time'' of the ear can be defined as the reciprocal of a critical bandwidth of hearing. Using Zwicker's definition of critical bandwidth [278], the smallest critical bandwidth of hearing is approximately 100 Hz (below 500 Hz). Thus, the nominal integration time of the ear is 10ms below 500 Hz. (Using the equivalent-rectangular-bandwidth (ERB) definition of critical bandwidth [163,245], longer values are obtained). At a 50 kHz sampling rate, this is 500 samples. Therefore, FIR filters shorter than the ear's ``integration time,'' i.e., perceptually ``instantaneous,'' can easily be hundreds of taps long (as discussed in the next section). FFT convolution is consequently an important implementation tool for FIR filters in digital audio applications.

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.