a) The impulse response of a LTI system is given as h(t) = ße¯t cos(Nj+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)=e*u(t) and g(t) = B cos(Q,t +g) = B cos2,(t+ Using the frequency convohtion property, or F(j0)*8(N±N,)=F(j[Q±Q,]) show that H(jN) = B- (a coso-N, sin g) +j(cosø)N (a+ jN)² +N; 1 F(jN) = a+ jN FcosD,)= πδ(Ω+Ω) + πδ(Ω-Ω,) Hint: To obtain the same result use also the time shifting property for cos(N,t + g) = cosN,(t+L). b) If H(jN)= 1-N°+ jN evahate a , B, q and N, and express h(t) using these vahes.

a) The impulse response of a LTI system is given as h(t) = ße¯t cos(Nj+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)=eu(t) and g(t) = B cos(Q,t +g) = B cos2,(t+ Using the frequency convohtion property, or F(j0)8(N±N,)=F(j[Q±Q,]) show that H(jN) = B- (a coso-N, sin g) +j(cosø)N (a+ jN)² +N; 1 F(jN) = a+ jN FcosD,)= πδ(Ω+Ω) + πδ(Ω-Ω,) Hint: To obtain the same result use also the time shifting property for cos(N,t + g) = cosN,(t+L). b) If H(jN)= 1-N°+ jN evahate a , B, q and N, and express h(t) using these vahes.

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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