Signals and SystemsD E F x(t) = 1+x, (t) + x,(t) + x,(t) = 1+cos ( fiz tcns ( 87 t) + cns (147t +).x, (t), x2(t) and x, (t) are delayed by different amounts of time (from the origin).a)Calculate these delays.How can you show that x(t) is a periodic signal. Find the fundamental frequency andperiod T, uf x(t).Mathematically explain which harmonics exist and which are nonexistent in x(t).We know that the Fourier-series expansion of any periodic signal can be given in thefollowing three fumms:b)c)d)f(t) = a, +> (ae cos(kl,t) + b, sin(kant)}k-1= ao + E, vat + b {cos(klot – o)} = a, + E, 2|c4l?{cos(kh,t – )}= E-C peikilatBy comparing x(t) with f(t) find a, h, Pk and c. Fill in the blanks in the tablebelow (including k), showing every slep of your caleulations.kklobrCKe)Fomulate x(t) in the above three forms.Draw the magnitude and phase frequency spectrums of x(t).Compute the average and RMS values of x(t).g)

xt=1+x1t+x2t+x3t=1+12cos6πt-π6+16cos8πt+17cos14πt+π3

x(t) = 1+x, (t) + x,(?) + x,(t) = 1+cos (6zt -+ cns (8r t) + cns ( 14z t +). x, (t), x,(t) and x, (t) are delayed by differeat amounts of time (from the origin). Calculale these delays. a) b) How can you show that x(t) is a periodic signal. Find the fundamental frequency and period T, of x(t). Mathematically explain which harmonics exist and which are nonexistent in x(t). c)

x(t) = 1+x, (t) + x,(?) + x,(t) = 1+cos (6zt -+ cns (8r t) + cns ( 14z t +). x, (t), x,(t) and x, (t) are delayed by differeat amounts of time (from the origin). Calculale these delays. a) b) How can you show that x(t) is a periodic signal. Find the fundamental frequency and period T, of x(t). Mathematically explain which harmonics exist and which are nonexistent in x(t). c)

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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