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Lecture 4: Using Fourier for Signal Analysis

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Suppose we have a system with transfer function $H(s)$ and a periodic input signal $f(t)$ . 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 $f(t)$ in terms of sinusoids, then use the properties of L.T.I. systems. Specifically, if
\begin{displaymath}f(t) = C_0 + \sum_{n=1}^\infty C_n \cos(n\omega_0 t + \theta_n). \end{displaymath}

then the output will be the sum of the responses due to each input:
\begin{displaymath}y(t) = C_0 H(0) + \sum_{n=1}^\infty C_n \vert H(jn\omega_0)\vert
\cos(n\omega_0 t + \theta_n + \angle H(jn\omega_0))

Discuss what happens in terms of filtering. In the homework you will work an example of this.
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, May 23). Lecture 4: Using Fourier for Signal Analysis. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: This work is licensed under a Creative Commons License Creative Commons License