Multirate Digital Signal Processing - Digital Signal Processing: An Introduction with MATLAB and Applications - page 209

Chapter 5
Multirate Digital Signal Processing
5.1 Introduction
The digital signal processing systems presented to date in this topic have been
single-rate systems, as the sampling rate has been fixed. There are, however, many
applications where it is necessary to change the sampling rate of the signal at
different stages in the signal processing chain. Such discrete-time systems are
referred to as Multirate Systems. There are varying reasons for wanting to change
the sample rate. In some applications it is changed to reduce computation, while at
other times it is changed to improve accuracy and mitigate against quantization
errors. At other times again, the sample rate may be changed to conserve band-
width. In all sampling rate alterations, however, it will be assumed that the Nyquist
criterion is always met and that there is therefore no aliasing.
Multirate systems play a particularly pivotal role in the areas of filter banks,
digital to analog conversion, de-noising, and compression.
This chapter reviews the fundamentals of multirate signal processing and
introduces some important multirate DSP applications.
5.2 Basic Elements of Multirate Processing
Multirate DSP systems require sampling-rate conversion at various stages of the
processing chain, and this conversion is usually achieved with either decimation
(i.e., sample rate reduction) or interpolation (sample rate increase). To perform
decimation and interpolation one typically uses three basic building blocks,
namely linear time invariant (LTI) low-pass filters, down-samplers and the up-
samplers.
The following sub-sections discuss the implementation of decimation and
interpolation, in both the time domain and frequency domains. Throughout these
sub-sections it will be assumed that the sampling rate of the original signal is f s .