#### 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
[305], 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 [179,269], 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.

**Next Section:**

Example 1: Low-Pass Filtering by FFT Convolution

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Pictorial View of Acyclic Convolution