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4) Using the Fourier transform pair FT sin NT u(t + T) – u(t - T) 2T NT And FT properties, compute the Fourier transforms of a) x1(t) = -u(t + 3) + 2u(t + 1) – u(t – 1) b) x2(t) = u(2t – 4) – u(2t + 4) c) x3 (t) = sin(wot)/t %3D

4) Using the Fourier transform pair FT sin NT u(t + T) – u(t - T) 2T NT And FT properties, compute the Fourier transforms of a) x1(t) = -u(t + 3) + 2u(t + 1) – u(t – 1) b) x2(t) = u(2t – 4) – u(2t + 4) c) x3 (t) = sin(wot)/t %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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4) Using the Fourier transform pair sin NT FT u(t + T) – u(t – T) 2T And FT properties, compute the Fourier transforms of a) x1 (t) = -u(t + 3) + 2u(t + 1) – u(t – 1) b) x2(t) = u(2t – 4) – u(2t + 4) c) x3 (t) = sin(w,t)/t Table 5.1 Basic properties of the Fourier transform Expansion/contraction x(at), a #0 la () Reflection x(-1) X(-2) Parseval's E, = (dt E = Duality X(t) d"x(1) 27 x(-2) Differentiation (ja" X (2) di" Integration x(t')dr X (2) +xX(0)8(2) Shifting x(t-a), elof x(1) ejan X2), X (2-20) Modulation x(t)cos(2,1) Periodie x(1) =EXLet x (2) = 2 X48(2- k2) 0.5[X(2-2)+X 2+2,)] Symmetry x(t) real |X(2)| =|X(-2). ZX(2) =-LX(-2) Z(2) = X(2)Y(2) Convolution 2t) =[x* y](t)
Transcribed Image Text:4) Using the Fourier transform pair sin NT FT u(t + T) – u(t – T) 2T And FT properties, compute the Fourier transforms of a) x1 (t) = -u(t + 3) + 2u(t + 1) – u(t – 1) b) x2(t) = u(2t – 4) – u(2t + 4) c) x3 (t) = sin(w,t)/t Table 5.1 Basic properties of the Fourier transform Expansion/contraction x(at), a #0 la () Reflection x(-1) X(-2) Parseval's E, = (dt E = Duality X(t) d"x(1) 27 x(-2) Differentiation (ja" X (2) di" Integration x(t')dr X (2) +xX(0)8(2) Shifting x(t-a), elof x(1) ejan X2), X (2-20) Modulation x(t)cos(2,1) Periodie x(1) =EXLet x (2) = 2 X48(2- k2) 0.5[X(2-2)+X 2+2,)] Symmetry x(t) real |X(2)| =|X(-2). ZX(2) =-LX(-2) Z(2) = X(2)Y(2) Convolution 2t) =[x* y](t)
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