TABLE OF CONTENTS Linear time-invariant systems operate at a single sampling rate i.e. the sampling rate is the same at the input and at the output of the system, and at all the nodes inside the system. Thus, in an LTI system, the sampling rate doesn't change in different stages of the system. Systems that use different sampling rates at different stages are called the multirate systems. The multirate techniques are used to convert the given sampling rate to the desired sampling rate, and to provide different sampling rates through the system without destroying the signal components of interest.
In this chapter, we consider the sampling rate alterations when changing the sampling rate by an integer factor. We describe the basic sampling rate alteration operations, and the effects of those operations on the spectrum of the signal.
Converting the sampling rate means that one discrete signal is converted into another discrete signal with a different sampling rate. Two discrete signals with different sampling rates can be used to convey the same information. For example, a bandlimited continuous signal x c( t) might be represented by two different discrete signals { x[ n]} and { y[ n]} obtained by the uniform sampling of the original signal x c( t) with two different sampling frequencies F T and F T'
where T= 1/ F T and T'=1/ F T' are the corresponding...
