The complete family of convolution forms for linear time invariant systems


The most common convolution technique for evaluating the output of linear time invariant systems is to convolve the system h(t) impulse response with the input x(t). A major extension of these concepts is presented whereby the convolution of the n th derivative (or integral) of the input x(t) can be convolved respectively with the n th integral (or derivative) of the h(t) impulse-response to yield the output. This extension of convolution theory not only leads to more powerful techniques for system analytical analyses, it also provides the basis for an elegant mathematical interpretation of representing x(t) signal models as expansion of x(t) into an infinite sum of infinitesimal singularity functions.

Publication Title

Computers in Education Journal

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