4. ALTI CT system has transfer functionH(s) =s² +1(s + 1)(s² + 2s + 17)Compute the steady-state and transient responses resulting when the input x(t) isa) x(t) = u(t), with zero initial conditionsb) x(t) = cost(t), t ≥ 0, with zero initial conditions TABLE 3.1 Properties of the Fourier TransformPropertyLinearityRight or left shift in timeTime scalingTime reversalMultiplication by a power of tMultiplication by a complex exponentialMultiplication by sin (wot)Multiplication by cos(wot)Differentiation in the time domainIntegration in the time domainConvolution in the time domainMultiplication in the time domainParseval's theoremSpecial case of Parseval's theoremDualityTransform Pair/Propertyax(t) + bv(t)→aX(w) + bV(w)x(tc)X(w)e-josex (at) < > ² x ( =) a >Xax(−1)→X(-w) = X(w)a>0d"t"x(t) → j" don X (w) n = 1, 2, ...dw"x(t)ejat →X(w - wo) wo realx(t) sin(wt) ↔ { [X(w + w) − X(w − w)]x(t) cos(wit) → [X(w + wo) + X(w − w)]din X(t) → (jw)"X(w) n = 1, 2,...1[x(x) dx → — X (w) + 7X (0)8(w)jwx(t) *v(t) →X(w)V(w)x(t)v(t) → __X(w)*V(w)[x(1)v(1) dt =1[~_* x²(1) dt = 2 /2TTX(t)→2πx(-w)[XV (oo) das1X (w) ² do-xxTABLE 3.2 Common Fourier Transform Pairs1, -∞ < t < ∞ → 2π8 (W)−0.5 + u(t) ↔ -jw1jwu(t) <> πδ(ω) +8(t) →18(tc)e-jwc, c any real number1jw + b²e-btu(t).ejut → 2πd (w - wo), wo any real numberτω2πP:(t)→7 sinc-b>07 sinc→2πp, (w)272|t|τω(1 - 2!!!) p.,(1)→ sinc²(e)Tsinc²(# )+2π(1 - 2!!)P, (c)2Tcos(wot) →T[8(w + wo) + d(w = wo)]cos(wat + 0)→π[e¯jªs(w + wo) + ejªs(w - wo)]sin(wot) → jπ[8(w + wo) − 8(w - wo)]sin(wat + 0) → jπ[e¯jªs(w + wo) — ejªts (w - wo)]

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4. ALTI CT system has transfer function H(s) = s² +1 (s + 1)(s² + 2s + 17) Compute the steady-state and transient responses resulting when the input x(t) is a) x(t) = u(t), with zero initial conditions b) x(t) = cost(t), t ≥ 0, with zero initial conditions

4. ALTI CT system has transfer function H(s) = s² +1 (s + 1)(s² + 2s + 17) Compute the steady-state and transient responses resulting when the input x(t) is a) x(t) = u(t), with zero initial conditions b) x(t) = cost(t), t ≥ 0, with zero initial conditions

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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