Published on Jun 05, 2023
Multirate systems have gained popularity since the early 1980. Multi-rate signal processing studies digital signal processing systems which include sampling 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.
In multirate digital signal processing the sampling rate of a signal is changed in order to increase the efficiency of various signal processing operations. Decimation, or Down-sampling, reduces the sampling rate, whereas expansion, or up-sampling, followed by interpolation increases the sampling rate.
In most applications multirate systems are used to improve the performance, or for increased computational efficiency. A key characteristic of multirate algorithms are their high computational efficiency. In many cases, these algorithms are the prime reason that an application can now be implemented economically using modern digital signal processors.
Multirate signal processing is used for the practical applications in signal processing to save costs, processing time, and many other practical reasons.
Some applications of multirate signal processing are:
• Up-sampling, i.e., increasing the sampling frequency, before D/A conversion in order to relax the requirements of the analog low pass antialiasing filter. This technique is used in audio CD, where the sampling frequency 44.1 kHz is increased fourfold to 176.4 kHz before D/A conversion.
• Various systems in digital audio signal processing often operate at different sampling rates. The connection of such systems requires a conversion of sampling rate.
Decomposition of a signal into M components containing various frequency bands. If the original signal is sampled at the sampling frequency fs (with a frequency band of width fs= 2, or half the sampling frequency), every component then contains a frequency band of width 1/2 fs=M only, and can be represented using the sampling rate fs=M . This allows for efficient parallel signal processing with processors operating at lower sampling rates. The technique is also applied to data compression in sub band coding , for example in speech processing, where the various frequency band components are represented with different word lengths.
• In the implementation of high-performance filtering operations, where a very narrow transition band is required. The requirement of narrow transition bands leads to very high filter orders. However, by decomposing the signal into a number of sub bands containing the pass band, stop band and transition bands, each component can be processed at a lower rate, and the transition band will be less narrow.
