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    Fourier transform and convolution

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    Please see the attach file, it take from "Optimization of electronic measurements module 4 text with experiments" by Howard V.Malmstadt

    © BrainMass Inc. brainmass.com October 10, 2019, 7:18 am ad1c9bdddf


    Solution Preview

    The transform integral is
    Note that the actual transform occurs when
    In our case
    To evaluate the integral we use the trigonometric identities:


    So the integral is now:


    This is a simple integral to evaluate and we get:

    For and the amplitude (left) and the Power spectrum (right) look like

    When we change T to 1s the amplitude they look like:

    As we see that the peak gets narrower and narrower, until it ...

    Solution Summary

    The solution shows how the convolution of two signals on the time domain translate to the frequency domain