Use MatLab to Generate 256 points of the following signals Xi (n) cos (0.1 n) u(

Question

Use MatLab to

Generate 256 points of the following signals Xi (n) cos (0.1 n) u(n) and X2(n)-[cos (0.1 n) + 0.2 cos (0.3 n) ] u(n) and determine the time response of these systems. Determine how the amplitude and phase of each component is affected by the filters in each signal. Add white Gaussian noise to the first signal xi(n) to yield signal- to-noise ratio (SNR) of 5dB 1 . Then, apply the noisy signal to these filters and evaluate thelir performance in trms of SNR inprovermnent and signal ecovery.

Explanation / Answer

In order to plot the spectra from FFT coefficients, you need following information:

First you have load the 256 coefficients into a MATLAB variable. For example, if you save the coefficient as variable y_fft, then the following lines of code will plot the spectra for you:

In above code, Fs is sampling frequency and Npoint_fft equals 256.

You can generate the signal in MATLAB and then plot spectra. Below is some code for signal generation and plotting:

To add white gaussian

x = -2:.002:2;

% Initail variables

M = 0;

V = 500*10^(-6);

% Creating a singal

T = -pi + (pi+pi)*rand(1,1);

S = (13.5)*cos(2*pi*x+T);

% Creating Noise singal

W = M+sqrt(V)*rand(1,2500);

% Adding Noise to signal // This doesn't work

SW = awgn(S,W,'measured');

% or this doesn't work too

SW = S + W;

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