# How to plot this signal?

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Negar on 20 Feb 2011
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

#### 1 Comment

Negar on 20 Feb 2011
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 ...

zohar on 20 Feb 2011
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)

Negar on 20 Feb 2011
Thank U a lot Zohar, I'll try it..

Negar on 20 Feb 2011
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 ...

zohar on 20 Feb 2011
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)

Negar on 20 Feb 2011
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?

#### 1 Comment

zohar on 21 Feb 2011
It's looks ok type help psd to figure out more about spectrum.psd.

Negar on 20 Feb 2011
ufffff by the way how did you type your code? I couldn't change the font like yours...