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Problem 13-4 An LTI filter is a 5-point running sum described by the difference equation y[n] = x[n]+[n-1]+[n−2]+[n−3]+[n−4]. (a) Obtain a closed-form expression for the frequency response of this system. (b) Determine the frequencies where the frequency response is zero in −0.5 < ƒ ≤ 0.5. (c) Suppose the input is x[n] = 7+8 cos(0.25πn) +9 cos(0.4πn) for-∞

Problem 13-4 An LTI filter is a 5-point running sum described by the difference equation y[n] = x[n]+[n-1]+[n−2]+[n−3]+[n−4]. (a) Obtain a closed-form expression for the frequency response of this system. (b) Determine the frequencies where the frequency response is zero in −0.5 < ƒ ≤ 0.5. (c) Suppose the input is x[n] = 7+8 cos(0.25πn) +9 cos(0.4πn) for-∞

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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Problem 13-4 An LTI filter is a 5-point running sum described by the difference equation y[n] = x[n]+[n-1]+[n−2]+[n−3]+[n−4]. (a) Obtain a closed-form expression for the frequency response of this system. (b) Determine the frequencies where the frequency response is zero in −0.5 < ƒ ≤ 0.5. (c) Suppose the input is x[n] = 7+8 cos(0.25πn) +9 cos(0.4πn) for-∞<n<∞. Obtain an expression for the output in the form y[n] = A + B cos(2π fon + ¢o). (d) Suppose that the input is 1[n] = (7+8 cos(0.25πn) +9 cos(0.4πn)) u[n], where u[n] is the unit-step signal. For what values of n is the output 31[n] equal to the output y[n] in part (c)?
Transcribed Image Text:Problem 13-4 An LTI filter is a 5-point running sum described by the difference equation y[n] = x[n]+[n-1]+[n−2]+[n−3]+[n−4]. (a) Obtain a closed-form expression for the frequency response of this system. (b) Determine the frequencies where the frequency response is zero in −0.5 < ƒ ≤ 0.5. (c) Suppose the input is x[n] = 7+8 cos(0.25πn) +9 cos(0.4πn) for-∞<n<∞. Obtain an expression for the output in the form y[n] = A + B cos(2π fon + ¢o). (d) Suppose that the input is 1[n] = (7+8 cos(0.25πn) +9 cos(0.4πn)) u[n], where u[n] is the unit-step signal. For what values of n is the output 31[n] equal to the output y[n] in part (c)?
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