i have used duality property in part b
and always remember rect function is even function means
rect(-t) = rect(t)
Sa is sampling function. and we know Sa(t) = (Sin(t))/t
please answer all parts 2. Find the inverse Fourier transform for the following signals. [30 points]...
Find the inverse Fourier transform for the following signals. X(e^jw) = 2 cos(w)
Find and plot the Fourier transforms of the following signals. (if the Fourier transform is a complex function, plot the magnitude absolute value) and phase (argument) parts separately) [70 points]. [Hint: You can use the time shifting property if applicable] 5, 0 <ts3 Xs(t)-〈0, otherwise
1. (20 points) Fourier Transform and Inverse Transform Problems: (a) Compute the Discrete-time Fourier transform of signal (b) Determine the signal having the following Fourier transform X(w)cos2w.
Problem 5: [9 Points) Find the inverse Fourier transform of the frequency functions, (a) c) x(a 2 -6 Problem 5: [9 Points) Find the inverse Fourier transform of the frequency functions, (a) c) x(a 2 -6
2. Calculate the inverse Fourier transform of X(cfw) = {2 2j 0 <W <T -2j -n<w < 3. Given that x[n] has Fourier transform X(@j®), express the Fourier transforms of the following signals in terms of X(el“) using the discrete-time Fourier transform properties. (a) x1[n] = x[1 – n] + x[-1 - n] (b) x2 [n] = x*[-n] + x[n]
(a) (20 points) Find the Fourier transform of each of the signals given below: Hint: you may use Fourier Transforms Table. i. xi(t) = 2rect (-) cos(107t) ii. x2(t) = e(2+33)t ul-t+1) i co(t) - S1+ cos(at), \t<1 iii. x3(t) = 0 otherwise iv. x4(t) = te-tu(t)
Please answer all questions with math detail 3. (21 points) Laplace Transform (a) (15 points) Find the Laplace transforms of the following signals and determine their region of convergence sinwot)-iu i. f(t) -i, e-2(t-3 2<t otherwise (b) (6 points) The Laplace transform of a causal signal x(t) is given by X (s) = s2 , ROC: Re{s) > -1 Which of the following Fourier transforms can be obtained from X(s) without actu- ally determining the signal x(t)? In each case,...
fourier analysis 2. (a) Find the Fourier sine transform of b) Write f(x) as an inverse sine transform Hint: Don't directly calculate F,[f (x)(w). Begin with showing the representation sin wxdw. x >0 ㄧㄨ and then interchanging x and w in the representation. Now look at it carefully, what does the equation tell you?
Please answer all parts no work needed if used matlab! Q1. Find Fourier transform for the following function, where A-30, and T-3.5 s. Evaluate its value at 45 rad/s 2A/3 A/3 t (s) 3 2773 T F(o)407 +j -871 Submit Answer Incorrect. Tries 1/5 Previous Tries
Please help with detailed steps [2] [8 points) Please use the inverse Fourier transform formula (2D continuous case) to obtain the Fourier transform of the Laplacian, F(V2) , v). (Express Fourier transform of the Laplacian as a function of u, V and F(u, v), where F(u, v) is the FT of f)