Properties of Fourier TransformJELMAAN FOURIER(Fourier Transform)OPERASIFUNGSI MASA(Operation)(Time Function)1f(t) = F(@)eiat dwF(@) = f(t)e-jut dtKelinaran (Linearity)Simetri (Symmetrty)af:(t) + bf2(t)f(t) evenaF,(w) + bF2(w)F(@) = 2| f(t) cos w t dtf(t) oddF(@)= -2j| f(t) sin w t dtAnjakan masaf(t – to)F(@)e¬jwto(Time shifting)Skalaan masaf(at)la|(Time scaling)Penjelmaan masa(Time Transformation)Kedualan (duality)f(at – to)1le-jwto/a|a|2nf(-w)aF(@)F(t)Skalaan amplitude(Amplitude Scaling)Pemodulatan (modulation)af (t)f(t)e]wotf(t) cos wo tF(@ – wo)(F(w + wo) + F(@ – w.)]f(t) sin wo t- [F (ω- ω) -F(ω+ ω,)]2jPelingkaran (convolution)fi(t) * f2(t)fi(t)f2(t)F, (@)F2(w)F,(@) * F2(w)2nKebedaan (differentiation)d"[f(t)](ja)*F(@)d"[F(@)]dt"(-jt)"f(t)dw"Kamilan (integration)f(t)dt: F (ω) + πF (0) δ (ω)jwBalikan masa (Time Reversal)f(-t)F*(@) = F(-w)d" F(@)G)".dwnPekali masa (Multiplication by t)t"f(t) (b)A linear time-invariant (LTI) system is shown in Figure Q1. A signal x(t) = rect(t) isapplied at the input of an ideal low pass filter with frequency response H1(@) =rect(o/47). The filtered signal of Y(@) is shown.(i)Illustrate graphically X(@), H1(@), E(@) and F(@).(ii)Determine the type and the specification of the filter transfer function, H2(m) inorder to obtain the filtered signal of y(1).E(@)F(@)x(t).H(0)H:(@)y(1)Y(@)cos 10zt-12n-1010r12nFigure Q1

(b) A linear time-invariant (LTI) system is shown in Figure Q1. A signal x(t) = rect(t) is applied at the input of an ideal low pass filter with frequency response Hi(@) rect(o/47). The filtered signal of Y(@) is shown. (i) Illustrate graphically X(@), Hi(@), E(@) and F(@). (ii) Determine the type and the specification of the filter transfer function, H2(m) in order to obtain the filtered signal of y(1).

(b) A linear time-invariant (LTI) system is shown in Figure Q1. A signal x(t) = rect(t) is applied at the input of an ideal low pass filter with frequency response Hi(@) rect(o/47). The filtered signal of Y(@) is shown. (i) Illustrate graphically X(@), Hi(@), E(@) and F(@). (ii) Determine the type and the specification of the filter transfer function, H2(m) in order to obtain the filtered signal of y(1).

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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