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-bands. These sub-bands are subsampled by a factor of N, so they are critically
sampled
Sample or samples may refer to:
Base meaning
* Sample (statistics), a subset of a population – complete data set
* Sample (signal), a digital discrete sample of a continuous analog signal
* Sample (material), a specimen or small quantity of so ...
.
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. If the ADC plus FPGA/ASIC interface implements a demultiplexer of the ADC samples in N internal FPGA/ASIC registers, 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
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or ''aliases'' of one another) when sampled. It also often refers to the distortion or artifact that results when ...
. Similar to the
MDCT
The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where ...
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
MPEG-1 Audio Layer I, commonly abbreviated to MP1, is one of three audio formats included in the MPEG-1 standard. It is a deliberately simplified version of MPEG-1 Audio Layer II (MP2), created for applications where lower compression efficiency ...
and
II,
Musepack
Musepack or MPC is an open source lossy audio codec, specifically optimized for transparent compression of stereo audio at bitrates of 160–180 (manual set allows bitrates up to 320) kbit/s. It was formerly known as MPEGplus, MPEG+ or MP+ ...
(which was based on MPEG-1 layer II), in
MPEG-1 Layer III with an additional MDCT, in
MPEG-4 AAC-SSR for the 4 band PQF bank, in
MPEG-4 V3 SBR
for the analysis of the upper spectral replicated band, and in
DTS.
PQF has an advantage over the very similar stacked
quadrature mirror filter In digital signal processing, a quadrature mirror filter is a filter whose magnitude response is the mirror image around \pi/2 of that of another filter. Together these filters, first introduced by Croisier et al., are known as the quadrature mirror ...
(QMF).
Delay
Delay (from Latin: dilatio) may refer to:
Arts, entertainment, and media
* ''Delay 1968'', a 1981 album by German experimental rock band Can
* ''The Delay'', a 2012 Uruguayan film
People
* B. H. DeLay (1891–1923), American aviator and acto ...
and computational effort are much lower.
A PQF filter bank is constructed using a base filter, which is a
low-pass
A low-pass filter is a filter that passes signals with a frequency lower than a selected cutoff frequency and attenuates signals with frequencies higher than the cutoff frequency. The exact frequency response of the filter depends on the filte ...
at fs/4N. This lowpass is modulated by N
cosine functions and converted to N
band-passes with a
bandwidth
Bandwidth commonly refers to:
* Bandwidth (signal processing) or ''analog bandwidth'', ''frequency bandwidth'', or ''radio bandwidth'', a measure of the width of a frequency range
* Bandwidth (computing), the rate of data transfer, bit rate or thr ...
of fs/2N.
The base lowpass is typically a
FIR filter with a length of 10*N ... 24*N taps. Note that it is also possible to build PQF filters using recursive
IIR filters.
Computation
There are different formulas possible. Most of them are based on the
MDCT
The modified discrete cosine transform (MDCT) is a transform based on the type-IV discrete cosine transform (DCT-IV), with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset, where ...
but are slightly modified.
References
Digital signal processing
Linear filters
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