Thanks ## Problem StatementGiven:\[ x(t) = \text{rect}(t) * \delta_1(t) \]where \( T = 1 \).**Task**: Use the CTFS (Continuous Time Fourier Series) table of transforms and properties to identify the CTFS harmonic function of the given periodic signal using the indicated representation time \( T \).## Answer Choices### Multiple Choice1. \(\text{rect}(t) * \delta_1(t) \overset{\text{FS}_1}{\longleftrightarrow} \delta_1[k]\)2. \(\text{rect}(t) * \delta_1(t) \overset{\text{FS}_1}{\longleftrightarrow} \delta_2[k]\)3. \(\text{rect}(t) * \delta_1(t) \overset{\text{FS}_1}{\longleftrightarrow} \delta_3[k]\) 4. \(\text{rect}(t) * \delta_1(t) \overset{\text{FS}_1}{\longleftrightarrow} \delta_4[k]\)This question involves choosing the correct Fourier Series harmonic function representation from the options provided.

It is given that: x(t)=rectt*δ1tT=1Now, the rectangular convolution with δ can be written as: rectt*δt=recttw*δtTo...........(i) Then, the Fourier series of recttw*1ToδtTo is: recttw*1ToδtTo↔FSwTosinc wTok..............(ii) Substituting To=1 and w=1 in equation (ii): rectt*δt↔FSsinc k.............(iii) Thus, here the sinc function only has non-zero values in this case, and for an integer harmonic number. When equal to, the value of the sinc function is the same as that of the δ(k) function. Now, substituting δ(k) in place of sinc k in equation (iii): rectt*δt↔FSδk Hence, the CTFS harmonic function of the given periodic signal using the representation time T indicated is δ(k). Therefore, option (c) is the correct option. (Ans)

Engineering

Electrical Engineering

x (t) = rect (t) * 81 (t) , T = 1 Using the CTFS table of transforms and the CTFS properties, Identify the CTFS harmonic function of the glven perlodic signal using the representation time Tindicated. Multiple Cholce rect (t) + 51 (t) 5 d1 [k]

x (t) = rect (t) * 81 (t) , T = 1 Using the CTFS table of transforms and the CTFS properties, Identify the CTFS harmonic function of the glven perlodic signal using the representation time Tindicated. Multiple Cholce rect (t) + 51 (t) 5 d1 [k]

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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