4. (a) Use the convolution theorem to show that otherwise (b) Let a > 0. Use the Fourier transfor...
4. Use the convolution property to derive the Fourier Transform of the signal else 4. Use the convolution property to derive the Fourier Transform of the signal else
Using the shift or stretch theorem find the Fourier transform of 1 for – 4 <t< -2 b(t) = { 0, otherwise 1 for – 1 <t < 1 given the transform of unit step function a(t) is ā(k) = 2 sin(k) k 0, otherwise b(k) =
3. (a) Let () be the rectangular pulse Il-oa()e-a, a 0 otherwise. Show that la sinc ka where sincx(note: in Engineering the alternate definition sincis often used). Use the symmetry of Fourier transform process to deduce that the Fourier transform of sinc i:s (b) Show that the' n-translates of sincTI are orthonormal 1 m n sinc π(x-m) sinc π(1-n) dr= 16 m メn. Hint: Use the shifting and scaling properties together with the Plancherel formula. 3. (a) Let () be...
please show all work ising convolution. integral is from 0 to t Use convolution theorem and solve y'-st 0 sin(t - 2)y()dA = cost, y(0) = 1. *integral is from zero to to t I
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:...
I really need help with Part B of this question Problem 2: a) If F(a) is the Fourier transform (FT) of a function qx), show that the inverse FT of ewb F(a) is q -b), with b a constant. This is the shift theorem for Fourier transforms. Hint: Y ou will need the orthogonality relation: where y-y) is the Dirac delta function] [ Joeo(y-y')dus2πδ(y-y'), b) Solve the diffusion equation with convection: vetneuzkat.aax au(x,t) аги, ди with-c < 鱸8: and ux,0)-far)....
Q4) Calculate the Fourier transform of the following time domain signals. Use the properties of the Fourier transform found in the "Properties of Fourier Transforms" table in textbook and the "Famous Fourier Transforms Table" in textbook instead of direct integration as much as possible to simplify your calculation wherever appropriate: 2-2
4. The Fourier transform of a rectangular pulse 1 비 r/2 0 otherwise is given by (a) Use pr(t) and properties of the Fourier transform to find the Fourier transform, D(w), of d(t) shown below, in terms of P(. First state the approach that you are using to find D(), then show all of the details. d(t)
Use the convolution theorem to find the inverse Laplace transform of the given function. 4 s' (s2 + 4) **** 14.30-0 $(2+4)
Need solution pls... 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)...