Explore BrainMass
Share

Explore BrainMass

    Fourier transform and convolution

    This content was COPIED from BrainMass.com - View the original, and get the already-completed solution here!

    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
    https://brainmass.com/physics/evaluations/fourier-transform-convolution-576005

    Attachments

    Solution Preview

    The transform integral is
    (1.1)
    Note that the actual transform occurs when
    In our case
    (1.2)
    To evaluate the integral we use the trigonometric identities:

    (1.3)
    Therefore:

    (1.4)
    So the integral is now:

    (1.5)

    This is a simple integral to evaluate and we get:

    (1.6)
    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

    $2.19