Pursuant to the first problem in the fast 1-D convolution series, this problem asks for the fast algorithm to compute the 1-D convolution with the same input-output shape.
There exists a fast 1-D convolution algorithm way more efficient than MATLAB's built-in conv function invoked in the form conv(u,v,'same'), and the performance improvement is more pronounced when length(u) and/or length(v) are large. Do you know how? Try it out.