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A filter bank is an array of band-pass filters that separates the input signal into several components, each one carrying a single frequency subband of the original signal. It also is desirable to design the filter bank in such a way that subbands can be recombined to recover original signal. The first process is called analysis, while the second is called synthesis. The output of analysis is referred as subband signal with as many subbands as there are filters in filter bank.

The filter bank serves to isolate different frequency components in a signal. This is useful because for most applications some frequencies are more important than others. For example these 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.

If the filters are combined with downsampling or upsampling then it is useful to represent that combination by a polyphase matrix. With the polyphase matrix you easily answer the question for the perfect reconstruction property of a filter bank.

• Wavelet
• Quadrature mirror filter
• Polyphase DFT, Polyphase FFT or WOLA (Weighted OverLap and Add), an efficient multi-channel filter bank method. see http://www.rfel.com/products/Products_polydft.asp for example.

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