So the first and last rows form a cyclic boundary? Easy peasy. :)
First, make up some garbage data.
R1 = rand(1,10);
A = [R1;rand(10);R1];
A is a 12x10 array, with the desired property.
Now you want to generate a Savitsky-Golay filter for this problem. Say a window of length 5. I'll arbitrarily pick a polynomial order as 1, so a linear model.
The filter is easy enough to generate, although I know what it will look like in advance.
M = pinv([ones(5,1),(-2:2)']);
F = M(1,:);
It should be [1 1 1 1 1]/5. A quick check verifies that fact:
F
F =
0.2 0.2 0.2 0.2 0.2
So we could now use conv2, with the convolution kernel of F.' to do the Savitsky-Golay. In order to force it to be cyclic though, just one more trick. Copy a couple of rows at the top and bottom, the number of which is based on the window length of the filter.
Ahat = [A(10:11,:);A;A(2:3,:)];
Afilt = conv2(Ahat,F.','valid');
Afilt
Afilt =
0.52952 0.60457 0.47513 0.50322 0.50705 0.7234 0.49297 0.50984 0.35622 0.69495
0.48703 0.75185 0.5751 0.57635 0.50425 0.71976 0.59578 0.4411 0.45476 0.72483
0.64224 0.57291 0.48437 0.55766 0.46489 0.67685 0.5031 0.32243 0.54791 0.63962
0.54804 0.41666 0.5809 0.67033 0.46353 0.678 0.54297 0.33712 0.60857 0.50357
0.51663 0.37418 0.47428 0.72159 0.3828 0.52293 0.70295 0.36182 0.70249 0.46339
0.37867 0.27461 0.40356 0.55024 0.40237 0.4292 0.75475 0.46202 0.76706 0.53382
0.40356 0.18139 0.27915 0.43136 0.47726 0.55353 0.60434 0.48566 0.68725 0.52565
0.30876 0.21009 0.26532 0.49641 0.58333 0.42446 0.55892 0.56039 0.56067 0.51497
0.25662 0.40364 0.29951 0.33418 0.57106 0.4526 0.64386 0.61905 0.48827 0.62547
0.30555 0.5171 0.3188 0.22171 0.626 0.5964 0.53163 0.64753 0.41491 0.6742
0.4321 0.59299 0.41492 0.34121 0.56364 0.67361 0.36325 0.58987 0.3041 0.7128
0.52952 0.60457 0.47513 0.50322 0.50705 0.7234 0.49297 0.50984 0.35622 0.69495
No problem. Afilt is a 12x10 array,
Afilt(1,:) == Afilt(end,:)
ans =
1×10 logical array
1 1 1 1 1 1 1 1 1 1
See there was no need to "adapt" the filter kernel. The trick was to properly expand the matrix itself.
