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Signals and Systems by Smarajit Ghosh

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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.,

 

image

 

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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