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(a) (i) Obtain the Fourier Transform for the signal y(t) shown below. 3 -2 -1 1 2 (ii) y(t) = sinc(nt)e/10t %3D

(a) (i) Obtain the Fourier Transform for the signal y(t) shown below. 3 -2 -1 1 2 (ii) y(t) = sinc(nt)e/10t %3D

Introductory Circuit Analysis (13th Edition)
Introductory Circuit Analysis (13th Edition)
13th Edition
ISBN:9780133923605
Author:Robert L. Boylestad
Publisher:Robert L. Boylestad
Chapter1: Introduction
Section: Chapter Questions
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Obtain the Fourier Transform for the signal y(t) shown below. (i) (a) y(t) -2 -1 2 (ii) y(t) = sinc(at)e10t (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 H(@) = rect(@/47). The filtered signal of Y(@) is shown. (i) Illustrate graphically X(m), H1(m), E(m) and F(m). (ii) Determine the type and the specification of the filter transfer function, H2(0) in order to obtain the filtered signal of y(1). E(@) F(@) x(1) H(0) H:(m) y(t) Y(m) cos 10nt -12n -10 10л 12n Figure Q1
Transcribed Image Text:Obtain the Fourier Transform for the signal y(t) shown below. (i) (a) y(t) -2 -1 2 (ii) y(t) = sinc(at)e10t (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 H(@) = rect(@/47). The filtered signal of Y(@) is shown. (i) Illustrate graphically X(m), H1(m), E(m) and F(m). (ii) Determine the type and the specification of the filter transfer function, H2(0) in order to obtain the filtered signal of y(1). E(@) F(@) x(1) H(0) H:(m) y(t) Y(m) cos 10nt -12n -10 10л 12n Figure Q1
Properties of Fourier Transform JELMAAN FOURIER (Fourier Transform) OPERASI FUNGSI MASA (Operation) (Time Function) 1 f(t) = F(@)eiat dw F(@) = f(t)e-jut dt Kelinaran (Linearity) Simetri (Symmetrty) af:(t) + bf2(t) f(t) even aF,(w) + bF2(w) F(@) = 2| f(t) cos w t dt f(t) odd F(@) = -2j| f(t) sin w t dt Anjakan masa f(t – to) F(@)e¬jwto (Time shifting) Skalaan masa f(at) la| (Time scaling) Penjelmaan masa (Time Transformation) Kedualan (duality) f(at – to) 1 le-jwto/a |a| 2nf(-w) aF(@) F(t) Skalaan amplitude (Amplitude Scaling) Pemodulatan (modulation) af (t) f(t)e]wot f(t) cos wo t F(@ – wo) (F(w + wo) + F(@ – w.)] f(t) sin wo t - [F (ω- ω) -F(ω+ ω,)] 2j Pelingkaran (convolution) fi(t) * f2(t) fi(t)f2(t) F, (@)F2(w) F,(@) * F2(w) 2n Kebedaan (differentiation) d"[f(t)] (ja)*F(@) d"[F(@)] dt" (-jt)"f(t) dw" Kamilan (integration) f(t)dt : F (ω) + πF (0) δ (ω) jw Balikan masa (Time Reversal) f(-t) F*(@) = F(-w) d" F(@) G)". dwn Pekali masa (Multiplication by t) t"f(t)
Transcribed Image Text:Properties of Fourier Transform JELMAAN FOURIER (Fourier Transform) OPERASI FUNGSI MASA (Operation) (Time Function) 1 f(t) = F(@)eiat dw F(@) = f(t)e-jut dt Kelinaran (Linearity) Simetri (Symmetrty) af:(t) + bf2(t) f(t) even aF,(w) + bF2(w) F(@) = 2| f(t) cos w t dt f(t) odd F(@) = -2j| f(t) sin w t dt Anjakan masa f(t – to) F(@)e¬jwto (Time shifting) Skalaan masa f(at) la| (Time scaling) Penjelmaan masa (Time Transformation) Kedualan (duality) f(at – to) 1 le-jwto/a |a| 2nf(-w) aF(@) F(t) Skalaan amplitude (Amplitude Scaling) Pemodulatan (modulation) af (t) f(t)e]wot f(t) cos wo t F(@ – wo) (F(w + wo) + F(@ – w.)] f(t) sin wo t - [F (ω- ω) -F(ω+ ω,)] 2j Pelingkaran (convolution) fi(t) * f2(t) fi(t)f2(t) F, (@)F2(w) F,(@) * F2(w) 2n Kebedaan (differentiation) d"[f(t)] (ja)*F(@) d"[F(@)] dt" (-jt)"f(t) dw" Kamilan (integration) f(t)dt : F (ω) + πF (0) δ (ω) jw Balikan masa (Time Reversal) f(-t) F*(@) = F(-w) d" F(@) G)". dwn Pekali masa (Multiplication by t) t"f(t)
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