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Suppose that the continuous-time input x (1) to the above system is given as x(1) = cos (16000r t) + cos(40007 t) + cos(1000r t). (a) What sampling rate is required such that no aliasing occurs for x(1)? f; = (b) Given that f - 10.000 samples/second plot the frequency spectrum for rln)

Suppose that the continuous-time input x (1) to the above system is given as x(1) = cos (16000r t) + cos(40007 t) + cos(1000r t). (a) What sampling rate is required such that no aliasing occurs for x(1)? f; = (b) Given that f - 10.000 samples/second plot the frequency spectrum for rln)

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
Problem 1P: Visit your local library (at school or home) and describe the extent to which it provides literature...
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PROBLEM: Ideal C-to-D Converter Ideal D-to-C Converter x(t) x[n] y(t) T = 1/fs T, = 1/fs Suppose that the continuous-time input x(t) to the above system is given as x(1) = cos(16000n t) + cos(40007 t)+ cos(10007t). (a) What sampling rate is required such that no aliasing occurs for x(1)? f, = (b) Given that f, = 10, 000 samples/second, plot the frequency spectrum for x[n]. Use ô for digital freq. -.87 -.67 -.4л —.2л .27 .47 .67 .87 (c) Given that x(t) = cos(26000rt) and f, = 10000 samples/second, write a simplified expression for the output y(t) in terms of cosine functions.
Transcribed Image Text:PROBLEM: Ideal C-to-D Converter Ideal D-to-C Converter x(t) x[n] y(t) T = 1/fs T, = 1/fs Suppose that the continuous-time input x(t) to the above system is given as x(1) = cos(16000n t) + cos(40007 t)+ cos(10007t). (a) What sampling rate is required such that no aliasing occurs for x(1)? f, = (b) Given that f, = 10, 000 samples/second, plot the frequency spectrum for x[n]. Use ô for digital freq. -.87 -.67 -.4л —.2л .27 .47 .67 .87 (c) Given that x(t) = cos(26000rt) and f, = 10000 samples/second, write a simplified expression for the output y(t) in terms of cosine functions.
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