Randy Yates wrote:
[snip]
>
>
> It's almost a matter of how you write it. The linear convolution is
>
> y[n] = x[n*M + 0*M - 0] * h[ 0*M + 0] + x[n*M + 0*M - 1] * h[ 0*M + 1] + ... + x[n*M + 0*M - (M-1)] * h[ 0*M + (M-1)]
> + x[n*M + 1*M - 0] * h[ 1*M + 0] + x[n*M + 1*M - 1] * h[ 1*M + 1] + ... + x[n*M + 1*M - (M-1)] * h[ 1*M + (M-1)]
> + ...
> + x[n*M + (K-1)*M - 0] * h[(K-1)*M + 0] + x[n*M + (K-1)*M - 1] * h[(K-1)*M + 1] + ... + x[n*M + (K-1)*M - (M-1)] * h[(K-1)*M + (M-1)]
>
> To get the "polyphase" version just look at this column-wise instead of row-wise.

I think I see where you're going with this, but I still have questions. In
order to get my brain wrapped around this equation I had to plug in some real
numbers. I chose M=3 and K=3. Unless I made a tragic error, the above reduces to:

y[n] = x[n*3 + 0] * h[0] + x[n*3 - 1] * h[1] + x[n*3 - 2] * h[2]
+ x[n*3 + 3] * h[3] + x[n*3 + 2] * h[4] + x[n*3 + 1] * h[5]
+ x[n*3 + 6] * h[6] + x[n*3 + 5] * h[7] + x[n*3 + 4] * h[8]

Still having trouble, so I plug in n=0 and try again:
y[0] = x[ 0] * h[0] + x[-1] * h[1] + x[-2] * h[2]
+ x[ 3] * h[3] + x[ 2] * h[4] + x[ 1] * h[5]
+ x[ 6] * h[6] + x[ 5] * h[7] + x[ 4] * h[8]

and again, with n=1:
y[1] = x[3] * h[0] + x[2] * h[1] + x[1] * h[2]
+ x[6] * h[3] + x[5] * h[4] + x[4] * h[5]
+ x[9] * h[6] + x[8] * h[7] + x[7] * h[8]

It looks to me like x needs both its rows and columns swapped. I'd be a lot
happier if I ended up with something like this:

y[1] = x[9] * h[0] + x[8] * h[1] + x[7] * h[2]
+ x[6] * h[3] + x[5] * h[4] + x[4] * h[5]
+ x[3] * h[6] + x[2] * h[7] + x[1] * h[8]

Again, I'm allowing ample room for the possibility that I'm wrong, so don't be
shy! Is your equation correct?

--
Jim Thomas Principal Applications Engineer Bittware, Inc
[email protected] http://www.bittware.com (603) 226-0404 x536
Hope springs occasionally.