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3- Determine the PSD for the randomly phased sinusoid X[n] = cos(2π(0.2)n + where - co

3- Determine the PSD for the randomly phased sinusoid X[n] = cos(2π(0.2)n + where - co

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
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3. Determine the PSD for the randomly phased sinusoid \( X[n] = \cos(2\pi(0.2)n + \Theta) \), where \( -\infty < n < \infty \) and phase \( \Theta \) is uniformly distributed on \( (0, 2\pi) \). Hint: The discrete-time Fourier transform of \( \exp(j2\pi f_0 n) \) for \( -\frac{1}{2} < f_0 < \frac{1}{2} \) is \( \delta(f - f_0) \) over the frequency interval \(-\frac{1}{2} \leq f \leq \frac{1}{2} \).
Transcribed Image Text:3. Determine the PSD for the randomly phased sinusoid \( X[n] = \cos(2\pi(0.2)n + \Theta) \), where \( -\infty < n < \infty \) and phase \( \Theta \) is uniformly distributed on \( (0, 2\pi) \). Hint: The discrete-time Fourier transform of \( \exp(j2\pi f_0 n) \) for \( -\frac{1}{2} < f_0 < \frac{1}{2} \) is \( \delta(f - f_0) \) over the frequency interval \(-\frac{1}{2} \leq f \leq \frac{1}{2} \).
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