Please provide simulations for all matlab code required, DO NOT SIMPLY WRITE IT

Question

Please provide simulations for all matlab code required, DO NOT SIMPLY WRITE IT OUT!!! It is all one part of a single problem, which is why I cannot post this in parts

Let N 64 denote the number of samples of the signal in time domain and frequency domain. For this length, generate the IDFT matrix W using MATLAB Let x be a time domain signal and let X denote its DFT. We have x - WX. Let X be a K-sparse signal with K-3. a vector X such that it has 3 non-zero coefficients. Assume the non zero coefficients are given by X(1)-2.X(3-5 and X(9)-12. Generate the tine domain signal using x -WX. Generate a 2N x 1 vector xp by concatenating the real and imaginary parts of x. Similarly, generate the 2N x N matrix Wp by concatenating the real and imaginary parts of W. Verify that xp -WpX. We wish to reconstruct X by taking only 5K -15 measurements of X. Observe that the number of measurements we are taking is much less than the length of the unknown signal X (which is 64 here). Let M denote a submatrix of Wp with 5K rows and 64 columns. The rows of M consist of 5K randomly picked rows from the matrix Wp. This can be done using the following sequence o f commands Let X'- MX denote the 5K measurements we take of the signal X. We find the sparse solution X of X by solving the 1 norm minimization problem minimize X subject to MX X' X 20 You may use the built-in MATLAB function linprog to solve this linear program. Verify that the optimal solution X of the linear program closely matches with the original signal X

Explanation / Answer

clc; clear all; close all;

X_freq = zeros(1,64); % Initialization

X_freq(1) = 2;

X_freq(3) = 5;

X_freq(9) = 12;

% IDFT Matrix

% Inverse Transform

x = W*X_freq;

xp = [real(x) imag(x)];

Wp = [real(W) imag(W)];

% Check

if xp == WpX_freq

disp('Confirmed');

else

disp('Not true');

M = randperm(2*N,15); % Random Permutation Matrix




%%%% Then Simply use linprog.

Related Questions

Navigate

• Browse (All)
• Browse P
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.