M<a a) Find the Fourier transform of b) Graph (x) and its Fourier transform fora c)...
Find the Fourier transform of f(x) = 1–x?, for -1 < x < 1 and f(x) = 0 otherwise. Hence evaluate the integral 6 * * cos sin cos des.
What is the Fourier transform of the following: f(0) = 3 sin wot for \t] < 57/W. elsewhere
Q2: Find the complex Fourier series (show your steps) - T < x <07 f(x) 0 < x < Q1: Find the Fourier transform for (show your steps) - 1<x< 0 Otherwise (хе f(x) = { 0,
*Fourier Series a) Skatch the graph of f(x) from -2n <x <3x. Hence, determine whether the function is even, odd or neither (3 marks) b) Gihen that b find a, and a,. Hence, write f(x)in a Fourier series (11 marks)
- Given the function f(x) = { 2, -1<x<i 10, otherwise find its Fourier sine transform g(a), such that f(x) g(a) sin oz da
(1 point) Find the appropriate Fourier cosine or sine series expansion for the function f(x) = sin(x), -A<<. Decide whether the function is odd or even: f(3) = C + C +
Find the required Fourier Series for the given function f(x). Sketch the graph of f(x) for three periods. Write out the first five nonzero terms of the Fourier Series. cosine series, period 4 f(0) = 3 if 0<x<1, if 1<x<2 1,
A sequence has the discrete-time Fourier transform 1 - a2 X(e) ae-jw)2(1- aejw) la| < 1 (a) Find the sequence r[n] (b) Calculate X(eju)cos(w)dw/27
3. (20pts.) Find the Fourier series of the function given 0- <x<0 x. 0<x<
where M=7 322-M2 4) Find the inverse - transform of F(z) = (2-1)(2-2M)' (15 marks) 0 t<-M/2 M <t< - 5) Show that the Fourier transform of function f(t) sin 7 s (10 marks) au 6) Show that u = ln(x2 + xy + y2) satisfies the partial differential equation x x ди +y 2. (7 marks) au 7) Solve the partial differential equation = e-cos(x) where at du x = 0, at =tet ax at and t = 0,...