optimization algorithms or any algorithms

Dear ALL

Hopefully you are keeping fine..

I need your help.

I want to generate a normal random sequence with mu=0 and sigma=1, and pass these sequence by filter as following:-

X=randn(1,100000); % generate normal random sequence.

A=[a1 a2 a3]; % the coefficients of the filter.

Y= filter(1,A,X);  %The sequence after passed on the filter.

NOW, I have my Data set called C, which is correlated normal random sequence.

SO, I need to adjust the coefficients of the filter ( A ) to give me the best value of y when RC=RY.

RC=xcorr(C,100); % the correlation coefficient of my data set C;

RY=xcorr(Y,100); % the desired correlation coefficient of Y;

*Could please to help me how can I find the best value of A which make RY is near to RC value, by any optimization algorithm. * Thanks in advance

RAYYAN

[Matt J]

How are you measuring "best"? How are you measuring "near"?

[RAYYAN]

Thanks Matt for your response I will calculate the error for every one as the following

E=mean(abs(RC-RY)^2)

the smallest value of E means the best one for me..

[RAYYAN]

Dear ALL This is the question in details.

I want to generate a normal random sequence with mu=0 and sigma=1, and pass these sequence by filter as following:-

X=randn(1,100000); % generate normal random sequence.
A=[a1 a2 a3]; % the coefficients of the filter.
Y= filter(1,A,X);  %The sequence after passed on the filter.

And then I will find the correlation coefficient of the first 100 points as following:

RY=xcorr(Y,100); % the correlation coefficient of the first 100 points of Y;

NOW, I have my Data set called C, which is correlated normal random sequence. And I will find also the correlation coefficient of the first 100 points for it.

RC=xcorr(C,100); % the correlation coefficient of my data set C;

Finally I will calculate the error of the mean value of between RC and RY by using

R=abs(RC-RY) % take the absolute value of difference result 
E=mean(R.*R) % find the mean of the  R square

SO, I need to adjust the coefficients of the filter ( A ) which give me the smallest value of error ( E ).

Thanks in advance.. RAYYAN

[Walter Roberson]

Your purpose is to find the coefficients of a two (three?) pole filter that will best transform an uncorrelated normal distribution to match the correlated normal distribution C ?

[RAYYAN]

Yes, exactly Mr.Walter

So, Could you please help me for that?

Answer 1

[Matt J]

You can solve for A algebraically using the Yule Walker equations

http://en.wikipedia.org/wiki/Autoregressive_model#Yule-Walker_equations

[RAYYAN]

Thanks Matt

I will check it, and let you know..