When and how to do zero-padding for a discrete convolution? - matlab

Question

I want to take the discrete convolution of two 1-D vectors. The vectors correspond to intensity data as a function of frequency. My goal is to take the convolution of one intensity vector B with itself and then take the convolution of the result with the original vector B, and so on, each time taking the convolution of the result with the original vector B. I want the final result to have the same length as the original vector B.
I am starting with a code in IDL that I am trying to modify to MATLAB. The relevant part of the code reads:
for i=1,10 do begin
if i lt 2 then A=B else A=Rt
n=i+1
Rt=convol(A,B,s,center=0,/edge_zero)
...
endfor
which I have rewritten in MATLAB
for i = 2:11
if i < 3
A = B; % indices start at 0, not 1
else
A = Rt;
end
n = i + 1;
% Scale by 1/s
Rt = (1/s).*conv(A,B);
...
end
But I am not sure how to incorporate the zero-padding that uses the edge_zero option. In IDL, the convolution calculates the values of elements at the edge of the vector as if the vector were padded with zeroes. The optional third option for the convolution function in MATLAB includes the option 'same', which returns the central part of the convolution of the same size as u for conv(u,v), but that doesn't seem to be the correct way about this problem. How do I do an analogous zero-padding in MATLAB?

Answer 1

Here is a code I needed for my doctoral research that I know does the zero padding correctly. I hope it helps.
function conv_out=F_convolve_FFT(f,g,dw,flipFlag),
if(nargin<4), flipFlag==0; end;
% length of function f to be convolved, initialization of conv_out, and padding p
N=length(f); conv_out=zeros(1,N); p=zeros(1,N);
% uncomment if working with tensor f,g's of rank 3 or greater
% f=F_reduce_rank(f); g=F_reduce_rank(g);
% padding. also, this was commented out: EN=length(fp);
fp = [f p]; gp = [g p];
% if performing convolution of the form c(w) = int(f(wp)g(w+wp),wp) = int(f(w-wp)gbar(wp),wp) due to reverse-order domain on substitution
if(flipFlag==1), gp=fliplr(gp); end;
% perform the convolution. You do NOT need to multiply the invocation of "F_convolve_FFT(f,g,dw,flipFlag)" in your program by "dx", the finite-element.
c1 = ifft(fft(fp).*fft(gp))*dw;
% if performing "reverse" convolution, an additional circshift is necessary to offset the padding
if(flipFlag==1), c1=circshift(c1',N)'; end;
% offset the padding by dNm
if(mod(N,2)==0), dNm=N/2; elseif(mod(N,2)==1), dNm=(N-1)/2; end;
% padding. also, this was commented out: EN=length(fp);
conv_out(:)=c1(dNm+1:dNm+N);
return