Jim Thomas <[email protected]> writes:

> Randy Yates wrote:
> > Jim Thomas <[email protected]> writes:
> [snip]
> >>Again, I'm allowing ample room for the possibility that I'm wrong, so
> >>don't be shy! Is your equation correct?
> > Nope! You're right. I had a sign problem in the x's. This corrects
> > that problem (hopefully
>
> > there are no others!):
> > 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)]
> > Thanks for the correction, Jim.
>
>
> That's better, and now I see what you mean. But... it seems to me
> that arranging the filter equation into rows and columns like this is
> somewhat artificial.

I agree. But it sure sounds impressive.

> At this point I'm just going to confuse people who already understand
> polyphase filters but aren't confident in their understanding, and for
> that, I apologize in advance. I guess I'm firmly in that same camp.

I think you've got more on the ball than you think.

> Each value of y depends on every filter tap, so I still don't see why
> it's polyphase. If this is polyphase, aren't ALL FIRs polyphase?

In a sense, yes. The difference between a "standard" FIR that is operating
in a system in which the input and output sample rate is the same and a
decimator is that you don't skip output computations.

Once again I come to the point where I must state, supporting Jim's
impression, that many things in DSP that "sound" very complex and
intimidating are, when you cut through to the bottom line, aren't all
that fancy. To me this "polyphase" stuff is in that category, but I
admit that I haven't studied the higher concepts like those in the
Vaidnayathan book on filter banks. Perhaps when you look at it from
a linear algebra point-of-view there is more to see.
--
Randy Yates
Sony Ericsson Mobile Communications
Research Triangle Park, NC, USA
[email protected], 919-472-1124