Index exceeds the number of array elements (4)

I am trying to write a script that will convolve two arrays (without using the conv function, just flipping and shifting then multiplying signals), and i have my script mostly written, however have an issue when i have a large signal convolved with a smaller one. It seems that my issue is with how im indexing i or y, however i dont really see any issue with it. please let me know what im doing wrong.

x = repmat([1:10 9:-1:2],1,20);
n1 = -180:179;

h = [1 -1];
n2 = [0 1];

%define k across n1 and n2
k = min(n1)+min(n2):max(n1)+max(n2);

%length of signals
lx = length(x);
lh = length(h);
lk = length(k);

%signals to convolve
xk = [x, zeros(1,lx)];
hk = [h, zeros(1,lh)];
y = [zeros(1,lk)];


%loop to shift through h
for i = 1:(lx+lh)-1
    y(i) = 0;
    for n = 1:lh
        if ((i-n)+1>0)
            y(i) = y(i) + (xk(n) * hk(i-n+1));
        end
    end
end

this yeilds the error:

Index exceeds the number of array elements (4).

Error in Project1Discrete (line 53)
            y(i) = y(i) + (xk(n) * hk(i-n+1));

however if i use a simpler input, like below, it runs and convolves just fine.

 x = [2 -3];
 n1 = [0 1];
 
 h = [3 -1 4];
 n2 = [-2 -1 0];

[Rik]

Out of curiosity: why are you avoiding using conv? It is just about the most optimized function that takes an appreciable amount of time that I have seen so far. My region growing function works based on it, and it actually saturates as many cores as I have (especially for larger (e.g. 3D) data).

[Ethan]

just a homework assignment... so have to see how convolution works behind the actual function

Answer 1

[Mahesh Taparia]

Hi

There was some error in the code. The error was there in assigning xk, hk and the range of n in the for loop. The below code will work.

x = repmat([1:10 9:-1:2],1,20);
n1 = -180:179;

h = [1 -1];
n2 = [0 1];

%define k across n1 and n2
k = min(n1)+min(n2):max(n1)+max(n2);

%length of signals
lx = length(x);
lh = length(h);
lk = length(k);

%signals to convolve
xk = [x, zeros(1,lh)];
hk = [h, zeros(1,lx)];
y = zeros(1,lk);


%loop to shift through h
for i = 1:(lx+lh)-1
%     y(i) = 0;
    for n = 1:lx
        if ((i-n)+1>0)
            y(i) = y(i) + (xk(n) * hk(i-n+1));
        end
    end
end

Moreover, you can use conv function to find convolution. Hope it will help!