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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

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

#### 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

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