Q.5a) The impulse response of a LTI system is given ash(t) = ße¯ª cos(Ni+9)u(t); a>0.Consider h(t) to be the product of the two signals f(t) and g(t) such thath(t) = f (t)g (t)wheref (t) =e¯d'u(t)andg(t) = B cos(2,t +@) = ß cos2,(t+Using the frequency convolution property, orF( jN)*5(N±Q,)=F(j[N±Q]) show that(a cos p-2, sin ø)+ j(cos p)N(a+ jN)² +N;H(jN)= ß-1F(jN) =F|cosΩ,) = πδ(Ω+Ω,) + πδ Ω-Ω,)a + jNHint: To obtain the same result use also the time shifting property forcos (2,t + p) = cos2,(t+-).b) IfH(jN) =1-N²+ jNevaluate a , ß, q and 2, and express h(t) using these values.c)Let the input to an LTI system with the transfer function given in part (b) be of the form1cos 5t +......141x(t)=+cost+- cos 3t +9.25Evaluate the first four terms of the Fourier series of the output y(t).

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Q.5 a) The impulse response of a LTI system is given as h(t) = ße¯d' cos(Nt+p)u(t); a>0. Consider h(t) to be the product of the two signals f(t) and g(t) such that h(t) = f (t)g (t) where f (t) =ed'u(t) and g(t) = B cos(2,t +p) = B cos2,(†+ Using the frequency convolution property, or F( jN)*8(N±Q)=F(j[N±Q,]) show that (a cos p-2, sin g)+ j(cos p)2 (a+ jN)² +N; H(jN) = B- 1 F(jQ) = F{cos Ω = πδ(Ω+Ω,) + πδ(Ω-Ω ) a + j2 Hint: To obtain the same result use also the time shifting property for cos (2,t +p) = cos2,(t+

Q.5 a) The impulse response of a LTI system is given as h(t) = ße¯d' cos(Nt+p)u(t); a>0. Consider h(t) to be the product of the two signals f(t) and g(t) such that h(t) = f (t)g (t) where f (t) =ed'u(t) and g(t) = B cos(2,t +p) = B cos2,(†+ Using the frequency convolution property, or F( jN)*8(N±Q)=F(j[N±Q,]) show that (a cos p-2, sin g)+ j(cos p)2 (a+ jN)² +N; H(jN) = B- 1 F(jQ) = F{cos Ω = πδ(Ω+Ω,) + πδ(Ω-Ω ) a + j2 Hint: To obtain the same result use also the time shifting property for cos (2,t +p) = cos2,(t+

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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