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Lecture 8: System Analysis Using the DTFT

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Schedule :: Transforms :: DTFT :: System Analysis :: Properties

For a discrete-time system with input signal $f[k]$ and impulse response $h[k]$ , the output is

\begin{displaymath}y[k] = f[k]*h[k]. \end{displaymath}

The discrete-time convolution theorem says that we can transform this to get

\begin{displaymath}Y(\Omega) = F(\Omega)H(\Omega). \end{displaymath}

Same sort of stuff we have seen all year long. We will finish the story by an example:

\begin{example}Let $h[k] = (0.5)^k u[k]$ and $f[k] = (0.8)^k u[k]$. Find
the ou...
...= [-\frac{5}{3}(0.5)^k + \frac{8}{3}(0.8)^k]u[k]. \end{displaymath}\end{example}
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 07). Lecture 8: System Analysis Using the DTFT. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/8_3node3.html. This work is licensed under a Creative Commons License Creative Commons License