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4. For a system described by the unit sample response h[n] = (1-a)*(na"'u[n]), where | a |< 1, a) obtain the DTFT H(eª) of this sequence. (Most of the work can be done using DTFT tables.) b) Plot the frequency function H(e^) (magnitude plot only) as a function ofN over the interval –7

4. For a system described by the unit sample response h[n] = (1-a)*(na"'u[n]), where | a |< 1, a) obtain the DTFT H(eª) of this sequence. (Most of the work can be done using DTFT tables.) b) Plot the frequency function H(e^) (magnitude plot only) as a function ofN over the interval –7

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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4. For a system described by the unit sample response h[n] = (1–a) (na""u[n]), where | a|<1, a) obtain the DTFT H(e*) of this sequence. (Most of the work can be done using DTFT tables.) b) Plot the frequency function H(e) (magnitude plot only) as a function of N over the interval -7 <Nsn. Do this for three values of the constant a, a= 0.95, a = 0.5, and a = 0.05. The three plots should be placed on the same graph. What type of filter does this system implement? 6. For the system described in Problem 4, without assigning a numerical value to the constant a, use convolution to obtain the output of the system when the input is just a unit step, namnely x[n] = u[n]. 7. Repeat the work of Problem 6 except that now the DTFT will be used to obtain the output of the system. Use tables for the transform computations as well as the inverse transforms. The answers in these two problems should be consistent. Plot the output signal specifically for the case a = 0.5. This is only for plotting purposes. Do not use this value to do the work in Problem 6 or this problem.
Transcribed Image Text:4. For a system described by the unit sample response h[n] = (1–a) (na""u[n]), where | a|<1, a) obtain the DTFT H(e*) of this sequence. (Most of the work can be done using DTFT tables.) b) Plot the frequency function H(e) (magnitude plot only) as a function of N over the interval -7 <Nsn. Do this for three values of the constant a, a= 0.95, a = 0.5, and a = 0.05. The three plots should be placed on the same graph. What type of filter does this system implement? 6. For the system described in Problem 4, without assigning a numerical value to the constant a, use convolution to obtain the output of the system when the input is just a unit step, namnely x[n] = u[n]. 7. Repeat the work of Problem 6 except that now the DTFT will be used to obtain the output of the system. Use tables for the transform computations as well as the inverse transforms. The answers in these two problems should be consistent. Plot the output signal specifically for the case a = 0.5. This is only for plotting purposes. Do not use this value to do the work in Problem 6 or this problem.
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