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Problem 12-1 Suppose that a[n] and h[n] are two finite-length sequences. h|n] is non-zero between No

Problem 12-1 Suppose that a[n] and h[n] are two finite-length sequences. h|n] is non-zero between No

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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Problem 12-1 Suppose that a[n] and h[n] are two finite-length sequences. h|n] is non-zero between No <n<N₁ and [n] is non-zero between N₂ <n< N3, e.g., the sequences look like the sketches shown below: hn xn No N₁ N₂ Να You do not know the values of these DT signals. You simply know where they are not equal to zero. Let yn rn hn] (the convolution of rn] and hin]). It can be shown that y|n] will also be a finite-length sequence if [n] and h[n] are both finite length. (a) Determine the location of the first non-zero point in y[n]. Your answer should be in terms of No, N1, N2, N3. (b) Determine the location of the last non-zero point in y[z]. Your answer should be in terms of No, N1, N2, N3. (c) Compute the convolution of the two signals shown below and use this result to verify your answers to parts a and b. hn=5n-5+5n-6]+5[n—7]+5[n—8]; = an] n-2]+25n-3]+5[n-4] Include sketches of an, hn], and y|n] as part of your solution.
Transcribed Image Text:Problem 12-1 Suppose that a[n] and h[n] are two finite-length sequences. h|n] is non-zero between No <n<N₁ and [n] is non-zero between N₂ <n< N3, e.g., the sequences look like the sketches shown below: hn xn No N₁ N₂ Να You do not know the values of these DT signals. You simply know where they are not equal to zero. Let yn rn hn] (the convolution of rn] and hin]). It can be shown that y|n] will also be a finite-length sequence if [n] and h[n] are both finite length. (a) Determine the location of the first non-zero point in y[n]. Your answer should be in terms of No, N1, N2, N3. (b) Determine the location of the last non-zero point in y[z]. Your answer should be in terms of No, N1, N2, N3. (c) Compute the convolution of the two signals shown below and use this result to verify your answers to parts a and b. hn=5n-5+5n-6]+5[n—7]+5[n—8]; = an] n-2]+25n-3]+5[n-4] Include sketches of an, hn], and y|n] as part of your solution.
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