"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').