(a) Given two sequences x[n] = [1,2,3,4,5,6] and y[n] = [4,5,6,1,2,3]. It is known that 2πmno 6 Y[m] = X[m]e . Find two values of no consistent with this information. (b) Let X [m] be the 8-point DFT of the sequence x[n] = [1, −1, 2, 3, −3, 0, 0, 0]. Let y[n] be 2πmno 6 a finite length sequence whose DFT Y [m] is related to X[m] as Y[m] = X[m]e where no = 3. Determine the sequence y[n]. (c) Let X[m] be the 6-point DFT of x[n] = [1,2,3,4, 5, 6]. Determine the sequence y[n] whose DFT Y[m] = X[{{−m))6]. (d) Let X[m] denote the 80-point DFT of x[n], 0 ≤ n ≤79. The sequence x1[n] is obtained by zero-padding a[n] to length 128. Determine mo such that Y[8] = X[mo]. (e) Let X[m], (0 ≤m ≤ 20) and Xd(w) respectively be the 21-point DFT and DTFT of a real-valued sequence {n}7-0 that is zero-padded to length 21. Determine all the choices that are definitely correct, - 4π 21 • X[19] = Xa( - • X[2] = X(- 4π 21 • X[12] = X( 4π - 21 • X[4] = X(-11) 21

(a) Given two sequences x[n] = [1,2,3,4,5,6] and y[n] = [4,5,6,1,2,3]. It is known that 2πmno 6 Y[m] = X[m]e . Find two values of no consistent with this information. (b) Let X [m] be the 8-point DFT of the sequence x[n] = [1, −1, 2, 3, −3, 0, 0, 0]. Let y[n] be 2πmno 6 a finite length sequence whose DFT Y [m] is related to X[m] as Y[m] = X[m]e where no = 3. Determine the sequence y[n]. (c) Let X[m] be the 6-point DFT of x[n] = [1,2,3,4, 5, 6]. Determine the sequence y[n] whose DFT Y[m] = X[{{−m))6]. (d) Let X[m] denote the 80-point DFT of x[n], 0 ≤ n ≤79. The sequence x1[n] is obtained by zero-padding a[n] to length 128. Determine mo such that Y[8] = X[mo]. (e) Let X[m], (0 ≤m ≤ 20) and Xd(w) respectively be the 21-point DFT and DTFT of a real-valued sequence {n}7-0 that is zero-padded to length 21. Determine all the choices that are definitely correct, - 4π 21 • X[19] = Xa( - • X[2] = X(- 4π 21 • X[12] = X( 4π - 21 • X[4] = X(-11) 21

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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