x Find the Fourier ransform f ог 2 (x) a elsewhere Hence evaluadte 5
(15 marks) Find the Fourier integral representation of \(f(x)=e^{-|x|}\) and hence show that$$ \int_{0}^{\infty} \frac{d t}{1+t^{2}}=\frac{\pi}{2} $$
*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)
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.
find fourier series of Question 3 Find Fourier series of f(x)= 0 if -55x<0 and f(x) = 1 if 0<x<5 which f(x) is defined on (-5,5).
(a) Find the Fourier series for f(x) = -x, -1<x<1 f(x+2) = f(x)
~ 〉' b, sin a. Find the Fourier coefficients for the function f(x)=| 7, 2 0 x〉 2 ~ 〉' b, sin a. Find the Fourier coefficients for the function f(x)=| 7, 2 0 x〉 2
(2) Consider the function f(x)- 1 (a) Find the Fourier sine series of f (b) Find the Fourier cosine series of f. (c) Find the odd extension fodd of f. (d) Find the even extension feven of f. (e) Find the Fourier series of fod and compare it with your result -x on 0<a < 1. in (a) (f) Find the Fourier series of feven and compare it with your result in (b)
3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal x(t) is X(f) - rect(f/ 2), find the Fourier Transform of the following signals using properties of the Fourier Transform: (a) d(t) -x(t - 2) (d) h(t) = t x( t ) (e) p(t) = x( 2 t ) (f) g(t)-x( t ) cos(2π) (g) s(t) = x2(t ) (h)p()-x(1)* x(t) (convolution) 3) (Fourier Transforms Using Properties) - Given that the Fourier Transform of a signal...
Find Fourier series of f(x) = 0 if -55x<0 and f(x) = 1 if 0<x<5 which f(x) is defined on (-5,5). Attach File Browse My Computer for Copyright Cleared File Browse Content Collection
1 a) 1) Sketch from (-3,3) and find the Fourier Series of f(x)= f(x+2) = f(x) xif -1 < x < 0 -X if 0 < x < 1 크 a) Apply the Fourier Convergence theorem to your result with an appropriate value of x to evaluate the sum: 1 (2n – 1)2 n=1