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Convolution of two functions

Hi, at university we were taught the convolution of two functions and their use in Fourier transforms by the way of the convolution theorem. Obviously I can how this can be useful, however, I can't see myself ever spotting that a function happens to be a convolution and what two functions make it up. So I'm wondering if there is something I'm missing here, is there a trick in spotting that a function is in fact a convolution or is it just pot luck that you happen to have come across it before? Thanks in advance.
Original post by Aiden223
Hi, at university we were taught the convolution of two functions and their use in Fourier transforms by the way of the convolution theorem. Obviously I can how this can be useful, however, I can't see myself ever spotting that a function happens to be a convolution and what two functions make it up. So I'm wondering if there is something I'm missing here, is there a trick in spotting that a function is in fact a convolution or is it just pot luck that you happen to have come across it before? Thanks in advance.
You are not missing anything.

Any function can be decomposed into a series of summed functions. This is the basis of Fourier analysis. In that sense, decomposition is the analogue to finding the integer factors of a number.

In other words there will be several solutions.

For instance in DSP systems, the impulse function (Dirac-delta function scaled and shifted) is used to decompose (model) a complex waveform (time domain) into a series of summed and weighted impulses. i.e. the mathematical description of the time-domain Analogue to Digital conversion process.

A different decomposition of the same waveform may use a Fourier cosine. i.e. yielding a frequency domain spectrum analysis.

In other words, like so many other mathematical tools, convolution is a means to an end in the world of electronic and systems engineering. Mathematicians on the other hand, are free to play with convolution for the sake of it.
(edited 8 years ago)

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