filterbanken

Filterbanken are signal processing systems that decompose an input signal into a set of subbands using a bank of filters. Each filter isolates a portion of the spectrum while attenuating the rest, allowing subsequent processing to be performed on smaller, easier-to-handle pieces. In many designs a corresponding synthesis bank reconstructs the original signal from the processed subbands.

In digital implementations, the analysis bank is often followed by downsampling by the number of channels, reducing the data rate in each subband. After subband processing, upsampling and synthesis filtering recombine the subbands to form the output. Polyphase decomposition is a common and efficient framework for implementing filter banks, enabling efficient multirate filtering and potential perfect reconstruction. Banks can be uniform, with equal bandwidth subbands, or nonuniform, allocating bandwidth according to application needs. They may be critically sampled (no redundancy) or oversampled (redundancy can improve stability and separation of subbands). Filters can be finite-impulse-response (FIR) or infinite-impulse-response (IIR), and may be real- or complex-valued.

Applications of filterbanks span audio and communications. In audio, subband coding and perceptual coding use filter banks to allocate bits where they matter most, and to simplify processing. In communications, filter banks enable channelization and multirate processing, while adaptive or programmable banks support noise reduction and equalization. Related concepts include quadrature mirror filters and other polyphase or time–frequency filter-bank constructions, as well as transforms such as the MDCT used in modern codecs. Overall, filterbanks provide a versatile tool for splitting, processing, and reconstructing signals with controlled distortion.