How to Calculate Gaussian Distribution , mean, Median, Auto Corelation, Standard Deviation, Time Average of Signals Using Matlab

TASK 1

clear all

close all

%% TASK 1

% Generate random noise using Gaussian distribution for [10 100 1000 and

% 10000] samples and calculate mean and standard devation

% Signal 1 for 10-samples

signal1=randn(1,10);

ms(1)=mean(signal1);  % mean

stds(1)=std(signal1); % standard deviation

% Signal 2 for 100-samples

signal2=randn(1,100);

ms(2)=mean(signal2);  % mean

stds(2)=std(signal2); % standard deviation

% Signal 3 for 1000-samples

signal3=randn(1,1000);

ms(3)=mean(signal3);  % mean

stds(3)=std(signal3); % standard deviation

% Signal 4 for 10000-samples

signal4=randn(1,10000);

ms(4)=mean(signal4);  % mean

stds(4)=std(signal4); % standard deviation

display(sprintf('sample mean of 4 random signals are \n[%1.4f %1.4f %1.4f %1.4f] and \nstandard deviation in signals are \n[%1.4f %1.4f %1.4f %1.4f]',ms,stds))

%% TASK 2

% Plot Auto-correlation of all the 4 realizations and comment on your                                        TASK 2

ACR1=Auto_Cor(signal1);

ACR2=Auto_Cor(signal2);

ACR3=Auto_Cor(signal3);

ACR4=Auto_Cor(signal4);

subplot(2,2,1)

plot(ACR1);

title('Signal1 Autocorrelation plot');

xlabel('Lag');

ylabel('Normalized output');

subplot(2,2,2)

plot(ACR2);

title('Signal2 Autocorrelation plot');

xlabel('Lag');

ylabel('Normalized output');

subplot(2,2,3)

plot(ACR3);

title('Signal3 Autocorrelation plot');

xlabel('Lag');

ylabel('Normalized output');

subplot(2,2,4)

plot(ACR4);

title('Signal4 Autocorrelation plot');

xlabel('Lag');

ylabel('Normalized output');

%% TASK 3

% Comment on the mean ergodicity of the signals

erg1=ergo_check(signal1);

erg2=ergo_check(signal2);

erg3=ergo_check(signal3);

erg4=ergo_check(signal4);

figure

subplot(2,2,1)

plot(erg1);

title('signal1 moving average');

subplot(2,2,2)

plot(erg2);

title('signal2 moving average');

subplot(2,2,3)

plot(erg3);

title('signal3 moving average');

subplot(2,2,4)

plot(erg4);

title('signal4 moving average');

%% Comments

display(sprintf('moving average of 4 random signals are \n[%1.4f %1.4f %1.4f %1.4f]',erg1(end),erg2(end),erg3(end),erg4(end)))

display(sprintf('Increasing number of samples in the realization shows that the signal \nbecome more random and its

TIME AVERAGE

TASK 3

M=500;

T=250;

t1=0:4*T+1

for n=1:M

        random_variable=a + (b-a).*rand(1,1);

Xt=sqrt(2)*cos(2*pi*0.004*t1+random_variable);

Xwt = awgn(Xt,1);

end

Rt=TA(Xwt,T);

plot(Rt);

function [ Rt ] = TA( X ,T)

for td=-T:T

    Rt(td+T+1)=0;

    for t=T:3*T+1

        Rt(td+T+1)=Rt(td+T+1)+(X(t)*X(t+td+1));

    end

    Rt(td+T+1)=Rt(td+T+1)/(2*T);

end

end

MATLAB CODE

x =linspace(pi,-pi);

t=1:100;

f=500;

fx=3*cos(f*2*pi*t+x)

% Signal 3 for 1000-samples

w=randn(1,100);  % mean

stds(3)=std(w); % standard deviation

ft=fx+w

subplot(2,2,4)

plot(fx)

title('COS');

subplot(2,2,3)

plot(w);

title('w(t)');

subplot(2,2,2)

plot(ft)

title('x(t)');

m=mean(ft);

subplot(2,2,1)

plot(m,t)

z=autocorr(ft)

plot(z)