Multi-rate digital signal processing

Multi-rate digital signal processing

Multi-rate signal processing studies digital signal processing systems which include sample rate conversion. Multirate signal processing techniques are necessary for systems with different input and output sample rates, but may also be used to implement systems with equal input and output rates.

Contents

Changing the sampling rate

The process of changing the sampling rate of a signal (resampling) is called downsampling if the sample rate is decreased and upsampling if the sample rate is increased. Integer rate changes are far more common than non-integer rate changes.

Downsampling

See also: Decimation (signal processing)

Downsampling a sequence x[n] by retaining only every Mth sample creates a new sequence xd[n] = x[nM]. If the original sequence contains frequency components above π / M, the downsampler should be preceded by a low-pass filter with cutoff frequency π / M. In this application, such an anti-aliasing filter is referred to as a decimation filter and the combined process of filtering and downsampling is called decimation.

Upsampling

See also: Interpolation

Upsampling a sequence x[n] creates a new sequence xe[n] where every Lth sample is taken from x[n] with all others zero. The upsampled sequence contains L replicas of the original signal's spectrum. To restore the original spectrum, the upsampler should be followed by a low-pass filter with gain L and cutoff frequency π / L. In this application, such an anti-aliasing filter is referred to as an interpolation filter and the combined process of upsampling and filtering is called interpolation.

Fractional rate changes

Changing the sampling rate of a signal by a rational fraction L / M can be accomplished by first upsampling by L, then downsampling by M. A low pass filter with cutoff min(π / L,π / M) is placed between the upsampler and downsampler to prevent aliasing.

Noble identities

The Noble identities describe the effect of interchanging sampling rate changes and filtering. Using (\downarrow M) to denote downsampling by a factor M and (\uparrow L) to denote upsampling by a factor L, we have

 (\downarrow M) H(z) = H(z^M) (\downarrow M)

and

  H(z) (\uparrow L) = (\uparrow L) H(z^L).

Polyphase Decomposition

The polyphase decomposition of a filter

H(z) = hnz n
n

is represented by

H(z) = \sum_{k = 0}^{M-1} H_k(z^M) z^{-k},

where

Hk(zM) = hk + nMz nM.
n

An important application of polyphase filters is in decimation, where the downsampling (\downarrow M) following the decimation filter can be moved before the subfilters Hk(zM), allowing each subfilter to be calculated at the lower sampling rate as Hk(z) (per the Nobel identities). Similarly, for interpolation, the upsampling (\uparrow M) can be moved after the subfilters, which are calculated as Hk(z).i

See also

References

  • Crochiere, Ronald E.; Rabiner, Lawrence R. (1983). Multirate Digital Signal Processing. Prentice-Hall. ISBN 0-13-605162-6. 
  • Oppenheim, Alan V.; Schafer, Ronald W. (1999). Discrete-Time Signal Processing (2nd ed.). Prentice-Hall. ISBN 0-13-754920-2. 

Wikimedia Foundation. 2010.

Игры ⚽ Поможем написать курсовую

Look at other dictionaries:

  • Digital signal processing — (DSP) 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. DSP includes… …   Wikipedia

  • Digital image processing — This article is about mathematical processing of digital images. For artistic processing of images, see Image editing. Paranal Observatory landscape after application of the city globe image technique. The Digital image processing is the use of… …   Wikipedia

  • Digital signal processor — A Digital Signal Processor chip found in a guitar effects unit. A digital signal processor (DSP) is a specialized microprocessor with an architecture optimized for the fast operational needs of digital signal processing.[1] …   Wikipedia

  • Digital Light Processing — The DLP Logo Further information: History of display technology Digital Light Processing (DLP) is a trademark owned by Texas Instruments, representing a technology used in some TVs and video projectors. It was originally developed in 1987 by Dr.… …   Wikipedia

  • Quantization (signal processing) — In digital signal processing, quantization is the process of approximating a continuous range of values (or a very large set of possible discrete values) by a relatively small set of discrete symbols or integer values.More specifically, a signal… …   Wikipedia

  • Multi-core processor — Diagram of a generic dual core processor, with CPU local level 1 caches, and a shared, on die level 2 cache …   Wikipedia

  • Digital Audio Broadcasting — For other digital audio broadcasting systems, see Digital radio.   Countries with regular services …   Wikipedia

  • Multi-core — A multi core processor (or chip level multiprocessor, CMP) combines two or more independent cores into a single package composed of a single integrated circuit (IC), called a die, or more dies packaged together. The individual core is normally a… …   Wikipedia

  • Digital synthesizer — A digital synthesizer is a synthesizer that uses digital signal processing (DSP) techniques to make musical sounds. Electronic keyboards make music through sound waves. Contents 1 History 2 Analog vs. digital 3 Bands using digital synth …   Wikipedia

  • Sample rate conversion — is the process of converting a (usually digital) signal from one sampling rate to another, while changing the information carried by the signal as little as possible. When applied to an image, this process is sometimes called image scaling.Sample …   Wikipedia

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”