Matrix form of Overlap-add

Question

We know overlap-add of a en-framed signal can be done easily by following code

function y = overlapAdd(frame, hop)
frameLen = size(frame, 1);
nframes = size(frame, 2);
xlen = frameLen + (nframes-1)*hop;
y = zeros(xlen, 1);
for l = 1 : nframes
    y(1+(l-1)*hop : frameLen+(l-1)*hop) = y(1+(l-1)*hop : frameLen+(l-1)*hop) + frame(:, l);
end

My question is, is there a computation form of overlap-add that uses solely matrix multiplication?

Since overlap-add is a linear operation, it can be represented by one or more matrix multiplications.

Answer 1

Forming a square matrix with mostly zeros but each input frame along rows, shifted by eg half a frame each, then summing (accumulating) each column seems like the most intuitive matrix operation here?

Eg

 tmp = …
[x1 x2 0 0 …
 0  y1 y2 0 …
 0  0  z1 z2]
Out = sum(tmp, 1);