4. Compute Fourier integral representation for f(x) = S\sinx[xST [x] > T = {leine $ "...
(1 point) If f(x) = { 6x, x39 8 x >9 Evaluate the integral 10 6.". f(x) dx |
IF Let x(t) Show that e 20" σ>0, and let (o) be the Fourier transform of x(t) .
IfX~ U(37,84), then P(X> 46|X<71) = 0.5319 0.8085 0.6923 0.7353
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2. Find the Fourier transform of f() = {6 1 – 12 \t <1 1t| > 1 Use the first shift theorem to deduce the Fourier transforms of e3jt (1-12) 11 <1 (a) g(t) 1t| > 1 {" (b)h() = {**"1 –1) "151 It| > 1 Answer: 63 4 cos o 4 sin o + -62 -4 cos(w – 3) (a) (0 – 3)2 -4 cos(w – j) (b) (w – j)2 + 4 sin(0 – 3)...
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1. Find the Fourier transform of 0 <t<2 (a) f(t) = 1+ -2<t<0 otherwise a > 0 (b) f(t) = Se-at eat t> 0 t < 0 () f(1) = { cost t> 0 t < 0 0 Answer: 1 - cos 20 (a) (b) 2a al + m2 (c) 1 + jo (1+0)2 + 1
QUESTION 9 Find the Laplace Transform of f(t)= - 1 if ts 4; f(t) = 1 if t> 0.
4-6. Using the Fourier transform integral, find Fourier transforms of the following signals: (a) xa(1)-1 exp(-α) u(t), α > 0; (b) xb(t) = u(t) u(1-t);
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a) f(t) = r|t| -1<t<1 t = 1 Compute the Fourier integral representations of f(t). It > 1 NI b) g(t (t, ostsi t = 1 Compute the Fourier cosine integral representation of g. t> 0 c) Compute the Fourier sine integral representation
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Evaluate the limit. sin 5x 10) lim 10) X>0 sinx A) -5 B) 1 C) 5 D) 0
Find the Laplace Transform of f(t)= -1 if t <= 4; f(t) = 1 if
t>4
Find the Laplace Transform of f(t) = - 1 ifts 4; f(t) = 1 if t> 4.