In
signal processing, a
filter bank is an array of
band-pass filters that separates the input signal into multiple components, each one carrying a single
frequency subband of the original signal. One application of a filter bank is a
graphic equalizer, which can attenuate the components differently and recombine them into a modified version of the original signal. The process of decomposition performed by the filter bank is called
analysis, and the output of analysis is referred to as a subband signal with as many subbands as there are filters in the filter bank. The reconstruction process is called
synthesis.
In
digital signal processing, the term
filter bank is also commonly applied to a bank of receivers. The difference is that receivers also down-convert the subbands to a low center frequency that can be re-sampled at a reduced rate. The same result can sometimes be achieved by
undersampling the bandpass subbands.
Another application of filter banks is
signal compression, when some frequencies are more important than others. After decomposition, the important frequencies can be coded with a fine resolution. Small differences at these frequencies are significant and a
coding scheme that preserves these differences must be used. On the other hand, less important frequencies do not have to be exact. A coarser coding scheme can be used, even though some of the finer details will be lost in the coding.
The
vocoder uses a filter bank to determine the amplitude information of the subbands of a modulator signal (such as a voice) and uses them to control the amplitude of the subbands of a carrier signal (such as the output of a guitar or synthesizer), thus imposing the dynamic characteristics of the modulator on the carrier.
FFT filter banks
A filter bank can be created by performing a sequence of
FFTs on overlapping blocks of the input data. A weighting function is applied to each block to control the shape of the frequency responses of the filters. Instead of a conventional FFT
window function, the weighting function is the
impulse response of an
FIR lowpass filter. The wider the shape of the frequency response
:- the more often the FFTs have to be done to satisfy the Nyquist sampling criteria (which is what distinguishes a filter bank from a spectrum analyzer), and
- the fewer filters that are needed to span the input bandwidth.
Eliminating unnecessary filters (i.e. decimation in frequency) can be accomplished most efficiently in the time-domain by summing subblocks of the weighted data-block, resulting in a smaller FFT size.
A special case occurs when, by design, the length of the subblocks is an integer multiple of the interval between FFTs. Then the FFT filter bank can be described in terms of one or more polyphase filter structures where the phases are recombined by an FFT instead of a simple summation. The number of subblocks is the impulse response length (or
depth) of each filter.
See also
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