December 2005
Intermediate to advanced
475 pages
12h 6m
English
Content preview from Signals and Systems
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1.16 CONVOLUTION
We have already studied properties like linearity, causality, shift invariance, stability etc. Since a majority of the discrete time systems in practice are linear and shift invariant. In many cases we take continuous systems as linear systems. these systems are termed as linear time invariant systems (LTI). To study LTI systems, linear convolution plays an important role. A sequence x(n) can be expressed as the weight of impulses i.e.,
If x(n) is applied as an input to a discrete time systems, the response y(n) of the system is given by
Similarly, for a continuous system,
Folding, shifting, multiplication ...
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