HW7.1 (A DTFS Puzzle) Consider a discrete-time signal x : Z → R having the following the properties: • • • a[n+4l] = x[n], VI, n∈Z . 2 Σα[n] = 2. n=-1 Σ(−1)"x[n] = 4. n=-1 2 • Σ x[n] cos [ẩn] = 2 Σ x[n] sin [n] = = 0. n=-1 n=-1 (a) Determine the complex exponential Fourier series coefficients X-1, X0, X1, and X2 for the signal x. From the coefficients, determine and provide a well- labeled plot for the signal x. (b) Based on your results from part (a), determine the fundamental period p and fundamental frequency wo of the signal x. Express x in terms of its DTFS co- efficients and complex exponentials of appropriate frequencies, and identify each coefficient and its corresponding harmonic frequency.

HW7.1 (A DTFS Puzzle) Consider a discrete-time signal x : Z → R having the following the properties: • • • a[n+4l] = x[n], VI, n∈Z . 2 Σα[n] = 2. n=-1 Σ(−1)"x[n] = 4. n=-1 2 • Σ x[n] cos [ẩn] = 2 Σ x[n] sin [n] = = 0. n=-1 n=-1 (a) Determine the complex exponential Fourier series coefficients X-1, X0, X1, and X2 for the signal x. From the coefficients, determine and provide a well- labeled plot for the signal x. (b) Based on your results from part (a), determine the fundamental period p and fundamental frequency wo of the signal x. Express x in terms of its DTFS co- efficients and complex exponentials of appropriate frequencies, and identify each coefficient and its corresponding harmonic frequency.

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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