# Lecture 4: Using Fourier for Signal Analysis

Suppose we have a system with transfer function
and a periodic input signal
.
What is the output signal? One way to do this, of course, is to convolve the input
signal with the impulse response. But we all know how much we love convolution,
and there is not a lot of insight to be gained from such a brute force computation.
Another approach is to represent
in terms of sinusoids, then use the properties of L.T.I. systems. Specifically,
if

then the output will be the sum of the responses due to each input:

Discuss what happens in terms of filtering. In the homework you will work an example of this.

then the output will be the sum of the responses due to each input:

Discuss what happens in terms of filtering. In the homework you will work an example of this.

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by the Contributing Authors.
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