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6. Determine the time-domain signals represented by the following FS coefficients: (a) X[k] = jó[k - 1] - jó[k + 1] +6[k - 3] +6[k +3], wo = 2π (b) X[k] = jók - 1]- jó[k + 1] +8[k - 3] +8[k+3], wo = 4T (c) X[k] =(-), wo = 1

6. Determine the time-domain signals represented by the following FS coefficients: (a) X[k] = jó[k - 1] - jó[k + 1] +6[k - 3] +6[k +3], wo = 2π (b) X[k] = jók - 1]- jó[k + 1] +8[k - 3] +8[k+3], wo = 4T (c) X[k] =(-), wo = 1

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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**Problem Description:** Determine the time-domain signals represented by the following FS (Fourier Series) coefficients: **(a)** \( X[k] = j\delta[k-1] - j\delta[k+1] + \delta[k-3] + \delta[k+3], \omega_0 = 2\pi \) **(b)** \( X[k] = j\delta[k-1] - j\delta[k+1] + \delta[k-3] + \delta[k+3], \omega_0 = 4\pi \) **(c)** \( X[k] = \left(-\frac{1}{3}\right)^{|k|}, \omega_0 = 1 \) --- **Explanation of Notations:** - \( X[k] \) represents the Fourier Series coefficients. - \( j \) denotes the imaginary unit. - \( \delta[k] \) refers to the discrete-time delta function. - \( \omega_0 \) is the fundamental angular frequency. In the problem, the main task is to analyze these Fourier Series coefficients and derive the corresponding time-domain signals. Each case has specific values for \( X[k] \) and \( \omega_0 \).
Transcribed Image Text:**Problem Description:** Determine the time-domain signals represented by the following FS (Fourier Series) coefficients: **(a)** \( X[k] = j\delta[k-1] - j\delta[k+1] + \delta[k-3] + \delta[k+3], \omega_0 = 2\pi \) **(b)** \( X[k] = j\delta[k-1] - j\delta[k+1] + \delta[k-3] + \delta[k+3], \omega_0 = 4\pi \) **(c)** \( X[k] = \left(-\frac{1}{3}\right)^{|k|}, \omega_0 = 1 \) --- **Explanation of Notations:** - \( X[k] \) represents the Fourier Series coefficients. - \( j \) denotes the imaginary unit. - \( \delta[k] \) refers to the discrete-time delta function. - \( \omega_0 \) is the fundamental angular frequency. In the problem, the main task is to analyze these Fourier Series coefficients and derive the corresponding time-domain signals. Each case has specific values for \( X[k] \) and \( \omega_0 \).
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