Question

Perform the following using Matlab For an additive Gaussian noise: a. Generate 4000 samples with mean value of 3 and variance of 9. b. Plot the sample values using two different ways. c. Determine the actual mean, variance, and standard deviation. d. Determine the median, mode, and range. e. Sketch the histogram. tle- enerate and plot the probability density function (pdf) and its corresponding cumulative distribution function (cdf) ror he M For the following two signals: / and y(t-V 0SIS1s 0otherwise 0 otherwise do the following: a. Generate and plot x and y) b. Generate and plot the autocorrelation function for each of x() and y). c. Generate and plot the cross correlation function. d. Generate and plot the power spectral density for each of x) and y) e. Generate and plot the cross power spectral density.

using matlab

Answer 1

clc
clear
close all

% gaussian / normal distibution

% part a
N = 4000;
varr = 9;
sd = sqrt(varr);
mu = 3;
gauss_samples = sd.*randn(N,1) + mu;

histrogram 1200 1000 800 S 600 400 200 0 -10 -5 0 5 10 15

pdf 0.3 0.25 0.2 X 0.15 0.1 0.05 0 0 500 1000 1500 2000 2500 3000 3500 4000

cdf 0.9 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1 2 0 500 1000 1500 2000 2500 3000 3500 4000

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% part b
figure
plot(gauss_samples,'-')
title(['additive guassian noise of mu = ' num2str(mu) ', var = ' num2str(varr)])
xlabel('sample (n)')
ylabel('value (x)')

figure
plot(gauss_samples,':')
title(['additive guassian noise of mu = ' num2str(mu) ', var = ' num2str(varr)])
xlabel('sample (n)')
ylabel('value (x)')

%part c
actual_mean = mean(gauss_samples)
actual_var = var(gauss_samples)
actual_std = sqrt(actual_var)

% part d

%median_value = median(gauss_samples)
sorted_samples = sort(gauss_samples);
if mod(N,2)~=0
median_value = sorted_samples(ceil(N/2))
else
median_value = (sorted_samples(N/2)+sorted_samples((N/2)+1))/2
end

mode_value = mode(gauss_samples)

% part e
figure
h = hist(gauss_samples);
hist(gauss_samples)
title('histrogram')
xlabel('x')
ylabel('frequancy of x')
grid on

%part f
%PDF
pdf = h./(sum(h));
x = linspace(0,N,numel(h));
figure
plot(x,pdf,'linewidth',2)
xlabel('x')
ylabel('p(X=x)')
title('pdf')
grid on

%CDF
cdf = cumsum(pdf)
x = linspace(0,N,numel(h));
figure
plot(x,cdf,'linewidth',2)
xlabel('x')
ylabel('p(X<=x)')
title('cdf')
grid on