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    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.
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    (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.
 
 
 
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