The most intuitive way I found to look at polyphase decimation (as I
learned it) was through the "commutator" structure shown in the
Crochiere book.

If you start out by writing out the convolution sum for every n.

y[n] = h[0]x[n] + h[1]x[n-1] + ... + h[N-1]x[n-N+1] , n=0,1,...

For a rate-M decimator, throw away every M output samples and then look
at your corresponding y[Mn] samples you wrote out above for a bunch of
different n values, you will see the structure.

Basically a direct-form decimator is similar to a standard FIR
implementation, but instead of computing one y output for each x input,
here you skip M samples in your x[n] history buffer for each y output
sample. Hence your computations are reduced by M.

For the polyphase approach, the commutator model basically does
something similar where you commutate your samples into your structure
- once you have injected M new samples into the filter you compute one
output point. It is just another way to look at the efficient
direct-form approach (but there are some subtle differences).

I had to put together a paper for some non-DSP engineers, it does show
the commutator model if you are interested:
http://www.hyperdynelabs.com/dsp/DSP...imizations.pdf

Dont go grading me on it, the paper was a quick write up!

Jim





Jon Harris wrote:
> "Randy Yates" <[email protected]> wrote in message
> news:[email protected]..
> >
> > 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.
>
> I agree with this. When I first about polyphase, it seemed to be
like a rather
> obvious optimization. Most of the inputs to your filter are zero, so
you don't
> bother including them in the calculation. Most of the outputs aren't
used
> anyway, so you don't bother computing them. Simple!
>
> One other point, I first learned about polyphase in the context of
sample rate
> conversion by a ratio of n/m, where 'the upsample by n' and
'downsample by m'
> are combined into a single filtering operation. In that case, you
end up with
> what looks like a standard FIR low-pass filter (sinc-like shape)
whose impulse
> response has been interpolated to a higher sample rate. But then you
end up
> only using a part (one phase) of that filter for every output sample.
To me,
> this rational conversion case is when you can really see the
polyphase technique
> in action and can get a grasp on why it is called polyphase
(literally 'many
> phases').