How to plot this signal?

Hi everyone, Can anybody tell me how to define this function and plot it in Matlab?

X(n) = X(n-1)+ 0.9 e(n)

where e(n) is a white,gaussian noise signal, and X(n) is a stationary, gaussian AR(1) process

[Negar]

Sorry Zohar but can you explain to me what you mean by 'not using first element' ? And why did you start n from 2 , and not from 1 ? I am not good at MATLAB at all ...

Answer 1

[zohar]

Hi Negar

l = 1000;% length of the signal
x = zeros(l,1);
Noise = 0.9*randn(l,1); % not using first element
% not using first element
% assuming x(0) = 0 or somthing else

for n = 2: length(x)
  x(n) = x(n-1)+ Noise(n);
end
% or you can use
x (2:length(x)) =   x (1:length(x)-1) + Noise(2:length(x));

plot(1:l,x)

I hope it's help you.

Answer 2

[Negar]

Thank U a lot Zohar, I'll try it..

Answer 3

[Negar]

Sorry but can you explain to me what you mean by 'not using first element' ? And why did you start n from 2 , and not from 1 ? I am not good at MATLAB at all ...

Answer 4

[zohar]

Hi Negar

l = 1000;% length of the signal
x = zeros(l,1);
Noise = 0.9*randn(l,1);

% sorry I meant the first element of x, x(1) not x(0) 
%assuming x(1) = 0 or somthing else

for n = 2: length(x)
  x(n) = x(n-1)+ Noise(n);
end

% or you can use
x (2:length(x)) = x(1:length(x)-1) + Noise(2:length(x));
plot(1:l,x)

I start with n=2 because x(1) allready defined 0.

Answer 5

[Negar]

Thank you so much Zohar , it really helped :)))))

Now , I have another question, how to find power spectral density of x(n)? I have made this code:

clc close all clear all

ro=0.9; % The nearest sample correlation l = 1000;% Length of the input signal x(n) x = zeros(l,1); E = randn(l,1); % Gaussian ,white noise signal e(n)

for n = 2: length(x) % Generation of the input signal x(n) = ro*x(n-1)+ sqrt(1-ro^2)*E(n);

end y =xcorr(x,x); % Autocorrelation function for x(n) plot(y); title('Autocorrelation function of input signal');

figure psd_x= psd(x); plot(psd_x); % power spectral density of signal x(n)

Is this a correct way to fin autocorrelation function and psd?

[zohar]

It's looks ok type help psd to figure out more about spectrum.psd.

Answer 6

[Negar]

ufffff by the way how did you type your code? I couldn't change the font like yours...

Answer 7

[Negar]

ok I think I found the answer, in order to fin psd, I should take FT of the autocorrelation function... I hope you will correct me if I am not right :)