Filter bank
Encyclopedia
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 (meaning analysis of the signal in terms of its components in each sub-band); 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, meaning reconstitution of a complete signal resulting from the filtering process.
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 (but less important) 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.
, the weighting function is the impulse response
of an FIR
lowpass filter. The wider the shape of the frequency response:
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.
Signal processing
Signal processing is an area of systems engineering, electrical engineering and applied mathematics that deals with operations on or analysis of signals, in either discrete or continuous time...
, a filter bank is an array of band-pass filters
Filter (signal processing)
In signal processing, a filter is a device or process that removes from a signal some unwanted component or feature. Filtering is a class of signal processing, the defining feature of filters being the complete or partial suppression of some aspect of the signal...
that separates the input signal into multiple components, each one carrying a single frequency
Frequency
Frequency is the number of occurrences of a repeating event per unit time. It is also referred to as temporal frequency.The period is the duration of one cycle in a repeating event, so the period is the reciprocal of the 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 (meaning analysis of the signal in terms of its components in each sub-band); 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, meaning reconstitution of a complete signal resulting from the filtering process.
In digital signal processing
Digital signal processing
Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...
, the term filter bank is also commonly applied to a bank of receivers. The difference is that receivers also down-convert
Digital down converter
In digital signal processing, a digital down-converter converts a digitized real signal centered at an intermediate frequency to a basebanded complex signal centered at zero frequency...
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
Undersampling
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate below the usual Nyquist rate In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate...
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
Coding
Coding may refer to:* Channel coding in coding theory* Line coding* Computer programming, the process of designing, writing, testing, debugging / troubleshooting, and maintaining the source code of computer programs...
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 (but less important) details will be lost in the coding.
The vocoder
Vocoder
A vocoder is an analysis/synthesis system, mostly used for speech. In the encoder, the input is passed through a multiband filter, each band is passed through an envelope follower, and the control signals from the envelope followers are communicated to the decoder...
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 functionWindow function
In signal processing, a window function is a mathematical function that is zero-valued outside of some chosen interval. For instance, a function that is constant inside the interval and zero elsewhere is called a rectangular window, which describes the shape of its graphical representation...
, the weighting function is the impulse response
Impulse response
In signal processing, the impulse response, or impulse response function , of a dynamic system is its output when presented with a brief input signal, called an impulse. More generally, an impulse response refers to the reaction of any dynamic system in response to some external change...
of an FIR
FIR
FIR or fir may refer to:*fir, a type of conifer tree*USCGC Fir, either of two buoy tenders of the United States Coast Guard*Fir , free ideal ring -Acronyms:* Falling In Reverse, a post-hardcore band...
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.
Filter banks as time-frequency distributions
In time-frequency signal processing, a filter bank is a special quadratic time-frequency distribution (TFD) that represents the signal in a joint time-frequency domain. It is related to the Wigner-Ville distribution by a two-dimensional filtering that defines the class of quadratic (or bilinear) time-frequency distributions. The filter bank and the spectrogram are the two simplest ways of producing a quadratic TFD; they are in essence similar as one (the spectrogram) is obtained by dividing the time-domain in slices and then taking a fourier transform, while the other (the filter bank) is obtained by dividing the frequency domain in slices forming bandpass filters that are excited by the signal under analysis.See also
- Discrete-time Fourier transform#Sampling the DTFT
- WaveletWaveletA wavelet is a wave-like oscillation with an amplitude that starts out at zero, increases, and then decreases back to zero. It can typically be visualized as a "brief oscillation" like one might see recorded by a seismograph or heart monitor. Generally, wavelets are purposefully crafted to have...
- SpectrogramSpectrogramA spectrogram is a time-varying spectral representation that shows how the spectral density of a signal varies with time. Also known as spectral waterfalls, sonograms, voiceprints, or voicegrams, spectrograms are used to identify phonetic sounds, to analyse the cries of animals; they were also...
- Time-frequency analysisTime-frequency analysisIn signal processing, time–frequency analysis comprises those techniques that study a signal in both the time and frequency domains simultaneously, using various time–frequency representations...
- Quadrature mirror filterQuadrature mirror filterIn digital signal processing, a quadrature mirror filter is a filter most commonly used to implement a filter bank that splits an input signal into two bands...
- Polyphase matrixPolyphase matrixIn signal processing,a polyphase matrix is a matrix whose elements are filter masks.It represents a filter bank as it is usedin sub-band coders alias discrete wavelet transforms.If h,g are two filters,then one level the traditional wavelet transform...