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Consider the signal x(1) sin 5071 TTI ². which we wish to sample with a sampling frequency of w, 150m to obtain a signal g(t) with Fourier transform G(jw). Determine the maximum value of for which it is guaranteed that G(jw) 75X(jw) for w≤ wo, where X(jw) is the Fourier transform of x(t).

Consider the signal x(1) sin 5071 TTI ². which we wish to sample with a sampling frequency of w, 150m to obtain a signal g(t) with Fourier transform G(jw). Determine the maximum value of for which it is guaranteed that G(jw) 75X(jw) for w≤ wo, where X(jw) is the Fourier transform of x(t).

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Consider the Signal** \[ x(t) = \left(\frac{\sin 50\pi t}{\pi t}\right)^2 \] We wish to sample this signal with a sampling frequency of \( \omega_s = 150\pi \) to obtain a signal \( g(t) \) with a Fourier transform \( G(j\omega) \). **Determine the Maximum Value of** \( \omega_0 \) **for which it is Guaranteed that:** \[ G(j\omega) = 75X(j\omega) \quad \text{for} \quad |\omega| \leq \omega_0 \] where \( X(j\omega) \) is the Fourier transform of \( x(t) \).
Transcribed Image Text:**Consider the Signal** \[ x(t) = \left(\frac{\sin 50\pi t}{\pi t}\right)^2 \] We wish to sample this signal with a sampling frequency of \( \omega_s = 150\pi \) to obtain a signal \( g(t) \) with a Fourier transform \( G(j\omega) \). **Determine the Maximum Value of** \( \omega_0 \) **for which it is Guaranteed that:** \[ G(j\omega) = 75X(j\omega) \quad \text{for} \quad |\omega| \leq \omega_0 \] where \( X(j\omega) \) is the Fourier transform of \( x(t) \).
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