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The Scientist and Engineer's
Guide to Digital Signal Processing
by Steven W. Smith
California Technical Publishing
ISBN 0-9660176-3-3 (1997)
Chapter 7. Properties of Convolution
- Common Impulse Responses
- Mathematical Properties
- Correlation
- Speed
- Summary of the key concepts
A linear system's characteristics are completely specified by the system's impulse
response, as governed by the mathematics of convolution. This is the basis of many
signal processing techniques. For example: Digital filters are created by designing an
appropriate impulse response. Enemy aircraft are detected with radar by analyzing a
measured impulse response. Echo suppression in long distance telephone calls is
accomplished by creating an impulse response that counteracts the impulse
response of the reverberation. The list goes on and on. This chapter expands on the
properties and usage of convolution in several areas. First, several common impulse
responses are discussed. Second, methods are presented for dealing with cascade and
parallel combinations of linear systems. Third, the technique of correlation is
introduced. Forth, a nasty problem with convolution is examined, the computation time
can be unacceptably long using conventional algorithms and computers.
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