how to plot the auto and cross correlation of walsh hadamard codes

i need a program to plot auto and cross corelation of walsh hadamard codes please

i have this program to generate a Walsh Hadamard Matrix of given codeword size=64

codeSize=64;

N=2;

H=[0 0 ; 0 1];

if bitand(codeSize,codeSize-1)==0

while(N~=codeSize)

N=N*2;

H=repmat(H,[2,2]);

[m,n]=size(H);

for i=m/2+1:m

for j=n/2+1:n

H(i,j)=~H(i,j);

end

end

end

else

disp('INVALID CODE SIZE:The code size must be a power of 2');

end

Answer 1

[vidyesh]

Hello Yas Mine,

To perform correlation between two signals, you can use ‘xcorr’ function.

In ‘xcorr’, if you provide only one input, output will be the autocorrelation of the signal for different lags.

H = hadamard(8);
[c,lags] = xcorr(H(2));

Here, ‘lags’ array stores the amounts of lags by which the signal is delayed, and ‘c’ array stores the corresponding values of the autocorrelation for that value of delays. Hence, after plotting ‘c’ against ‘lags’, we can visualize the values of autocorrelation at different delays.

Now, in our case, you are trying to find auto and cross correlation between the hadamard codes:

x1 = H(2,:);
x2 = H(3,:); 

Then use ‘xcorr’ function to find cross correlation between them.

[c,lags] = xcorr(x1,x2);
stem(lags,c); 

I would also advise to change 0 to -1 when you are first declaring 'H' and replace the line inside the nested for loop:

% H(i,j)=~H(i,j);

with

% H(i,j)= -1 *H(i,j);

Hope this will help you.

For more information you can follow these links.

Hadamard function: https://www.mathworks.com/help/signal/ug/discrete-walsh-hadamard-transform.html

Xcorr function: https://www.mathworks.com/help/matlab/ref/xcorr.html?searchHighlight=xcorr&s_tid=doc_srchtitle