Feedback by Tom Moir

Feedback by Tom Moir

Author:Tom Moir
Language: eng
Format: epub, pdf
ISBN: 9783030348397
Publisher: Springer International Publishing


(9.5)

In the case of the Laplace-Transform, we used this to prove that we can multiply the transfer-functions of LTI systems and is the foundation for most of our control-theory analysis. We can also write this as

(9.6)

The second property which we use is:

The Fourier-Transform of the product of two time-domain signals is the same as the convolution of their individual Fourier-Transforms.

In other words

(9.7)

where * represents convolution. We can also write (9.7) as

(9.8)

Now we can have a peek and see what effect multiplying a signal by a train of impulses has to a signal. We must take the FT of (9.2) and use the FT property of convolution in the frequency-domain.



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