8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the...
Answers are: 10. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 40 w2 - 13iw (b) Use Fourier transforms to solve dy -5t + 8y — 9е эH (). dt 15t H(t) 1 8t (а) (1) Н, 9 Then solve for 5iw (b) Apply the Formula of transform of derivatives to get: (iw+8)Y(w) Y (w) and take the inverse transform to have -8t у(0) — Зе 5 н(t) —...
Answers are: 9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of iw 4 + 9 w2 9 w2 (b) The function f(t) satisfies the integral equation: OO -4u Н(u) du + 6sgn(t) е З, f(t) 0- ft - u) е" = 4 e -OO Find the Fourier transform of the function f(t) and hence find the solution f(t) 7 "(1-)н, (b) Transform the equation by using the convolution Theorem:...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of iw 45iw(iw2 (b) The function f(t) satisfies the integral equation: f(t)2 f(t - u) sgn(u) du — 6е" H(). Find the Fourier transform of the function f (t) and hence find the solution f(t) The sign function sgn(t) = 1 if t 0, 0 if t 0 and -1 if t < 0 H(t) is the Heaviside unit step function...
9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t) satisfies the integral equation -4u f(t u) H(u) du 6sgn(t)e-3¢|. f(t) 4 Find the Fourier transform of the function f(t) and hence find the solution f(t) 9. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the inverse Fourier transform of 4 9+w2 9w2 (b) The function f(t)...
8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer. 8. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of sgn(t 1)e4t-1| (b) Hence, find the Fourier transform of 5i sgn(t 1) eit-4e-1| (Simplify your answer.
6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5). 6. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e sin (2(t5) H(t5) (b) Hence, find the Fourier transform of 6 e-3t-it sin (2(t +5)) H(t+5).
7. (a) Use the Tables of Fourier transforms, along with the operational theorems, to find the Fourier transform of -3t e H(t 4) (b) Hence find the Fourier transform of -6 е б-3)е н(t — 4)
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10 1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of 3s 7 82 -2s + 10 (b) Hence determine the inverse Laplace transform of 3s +7 -2s S2-2s10
1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16 1. (a) Using the Tables of Laplace transforms, along with the operational theorems, de- termine the inverse Laplace transform of s +3 82 6s 16 (b) Hence deduce the inverse Laplace transform of 83 -6s e s2 6s 16
(16 points] Use the scale change and time delay theorems along with the appropriate transform pairs to find the Fourier transforms of the following signals. a xa(t) = n(62 b. xy(t) = 2 sinc[2(t – 1)] C. Xo(t) = 4131 d. xa(t) = sinc?[(t – 3)/4]