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Find the frequency response of: <math>y[n] - \frac{3}{4}y[n-1] + \frac{1}{8}y[n-2] = 2x[n]</math> | Find the frequency response of: <math>y[n] - \frac{3}{4}y[n-1] + \frac{1}{8}y[n-2] = 2x[n]</math> | ||
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| + | First, we do the Fourier transform on both sides, which yields: | ||
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| + | :<math>Y(w) - \frac{3}{4}e^{-jw}Y(w) + \frac{1}{8}e^{-2jw}Y(w) = 2X(w)\,</math> | ||
Revision as of 10:41, 24 October 2008
If we were asked to compute the frequency response, one thing that we need to keep in mind is that, no matter how complexed the problem might look, we have to somehow arrange it into $ Y(w) = H(w)X(w) $ format. Obviously, $ H(w) $ is the frequency response. The following example would illustrate this:
Find the frequency response of: $ y[n] - \frac{3}{4}y[n-1] + \frac{1}{8}y[n-2] = 2x[n] $
First, we do the Fourier transform on both sides, which yields:
- $ Y(w) - \frac{3}{4}e^{-jw}Y(w) + \frac{1}{8}e^{-2jw}Y(w) = 2X(w)\, $
