Editing Polyphase quadrature filter

{{technical|date=January 2018}}
A '''polyphase quadrature filter''', or '''PQF''', is a [[filter bank]] which splits an input signal into a given number N (mostly a power of 2) of equidistant [[sub-band]]s. A factor of N subsamples these sub-bands, so they are critically [[sample (signal)|sampled]].<ref>{{Cite book|last=Rothweiler|first=J.|title=ICASSP '83. IEEE International Conference on Acoustics, Speech, and Signal Processing |chapter=Polyphase quadrature filters--A new subband coding technique |date=April 1983|volume=8|pages=1280–1283|doi=10.1109/ICASSP.1983.1172005}}</ref>
An important application of the polyphase filters (of FIR type) concerns the filtering and decimation of large band (and so high sample rate) input signals, e.g. coming from a high rate ADC, which can not be directly processed by an FPGA or in some case by an ASIC either. Suppose the ADC plus FPGA/ASIC interface implements a demultiplexer of the ADC samples in N internal FPGA/ASIC registers. In that case, the polyphase filter transforms the decimator FIR filter canonic structure in N parallel branches clocked at 1/N of the ADC clock, allowing digital processing when N=Clock(ADC)/Clock(FPGA).

This critical sampling introduces [[aliasing]]. Similar to the [[Modified discrete cosine transform|MDCT]] [[time domain alias cancellation]] the aliasing of polyphase quadrature filters is canceled by neighbouring sub-bands, i.e. signals are typically stored in two sub-bands.

Note that signal in odd subbands is stored [[frequency inverted]].

PQF filters are used in [[MPEG-1 Audio Layer I]] and [[MPEG-1 Audio Layer II|II]], [[Musepack]] (which was based on MPEG-1 layer II), in [[MP3|MPEG-1 Layer III]] with an additional MDCT, in [[MPEG-4 AAC-SSR]] for the 4 band PQF bank, in [[Spectral Band Replication|MPEG-4 V3 SBR]]
for the analysis of the upper spectral replicated band, and in [[Digital Theatre System|DTS]].

PQF has an advantage over the very similar stacked [[quadrature mirror filter]] (QMF). [[Propagation delay|Delay]] and computational effort are much lower.

A PQF filter bank is constructed using a base filter, which is a [[low-pass filter|low-pass]] at fs/4N. This lowpass is modulated by N [[cosine]] functions and converted to N [[band-pass filter|band-passes]] with a [[Bandwidth (signal processing)|bandwidth]] of fs/2N.

The base lowpass is typically a<!--n?--> [[finite impulse response|FIR]] filter with a length of 10*N ... 24*N taps. Note that it is also possible to build PQF filters using recursive [[infinite impulse response|IIR]] filters.

==Computation==

There are different formulas possible. Most of them are based on the [[modified discrete cosine transform|MDCT]] but are slightly modified.


==References==
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[[Category:Digital signal processing]]
[[Category:Linear filters]]


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