Polyphase quadrature filter
Encyclopedia
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.
This critical sampling introduces aliasing
. Similar to the 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 II
, Musepack
(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
(QMF). Delay
and computational effort are much lower.
A PQF filter bank is constructed using a base filter, which is a low-pass
at fs/4N. This lowpass is modulated by N cosine functions and converted to
N band-passes
with a bandwidth 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.
PQF filter parameter
but are slightly modified.
Filter bank
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...
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.
This critical sampling introduces aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...
. Similar to the MDCT
Modified discrete cosine transform
The modified discrete cosine transform is a Fourier-related transform based on the type-IV discrete cosine transform , with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset,...
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
MPEG-1 Audio Layer I, commonly abbreviated to MP1, is one of three audio formats included in the MPEG-1 standard. While supported by most media players, the codec is considered largely outdated, and replaced by MP2 or MP3....
and II
MPEG-1 Audio Layer II
MPEG-1 Audio Layer II or MPEG-2 Audio Layer II is a lossy audio compression format defined by ISO/IEC 11172-3 alongside MPEG-1 Audio Layer I and MPEG-1 Audio Layer III...
, Musepack
Musepack
Musepack or MPC is an open source lossy audio codec, specifically optimized for transparent compression of stereo audio at bitrates of 160–180 kbit/s...
(which was based on MPEG-1 layer II), in MPEG-1 Layer III
MP3
MPEG-1 or MPEG-2 Audio Layer III, more commonly referred to as MP3, is a patented digital audio encoding format using a form of lossy data compression...
with an
additional MDCT, in MPEG-4 AAC-SSR for the 4 band PQF bank, in MPEG-4 V3 SBR
Spectral band replication
Spectral band replication is a technology to enhance audio or speech codecs, especially at low bit rates and is based on harmonic redundancy in the frequency domain....
for the analysis of the upper spectral replicated band, and in DTS.
PQF has an advantage over the very similar stacked quadrature mirror filter
Quadrature mirror filter
In 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...
(QMF). Delay
Propagation delay
Propagation delay is a technical term that can have a different meaning depending on the context. It can relate to networking, electronics or physics...
and computational effort are much lower.
A PQF filter bank is constructed using a base filter, which is a low-pass
Low-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
at fs/4N. This lowpass is modulated by N cosine functions and converted to
N band-passes
Band-pass filter
A band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....
with a bandwidth of fs/2N.
The base lowpass is typically a FIR
Finite impulse response
A finite impulse response filter is a type of a signal processing filter whose impulse response is of finite duration, because it settles to zero in finite time. This is in contrast to infinite impulse response filters, which have internal feedback and may continue to respond indefinitely...
filter with a length of 10*N ... 24*N taps.
Note that it is also possible to build PQF filters using recursive IIR
Infinite impulse response
Infinite impulse response is a property of signal processing systems. Systems with this property are known as IIR systems or, when dealing with filter systems, as IIR filters. IIR systems have an impulse response function that is non-zero over an infinite length of time...
filters.
PQF filter parameter
Computation
There are different formulas possible. Most of them are based on the MDCTModified discrete cosine transform
The modified discrete cosine transform is a Fourier-related transform based on the type-IV discrete cosine transform , with the additional property of being lapped: it is designed to be performed on consecutive blocks of a larger dataset,...
but are slightly modified.