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