# why do we need Polyphase decimatation filter?

Started by February 5, 2006
```I did a decimator FIR filter simply by doing the convolution only once
every M' input sample.
for example M=3:
feed x0,feed x1, feed x2, convolution, feed x3,feed x4, feed x5,
convolution, feed x6,....

Then I find many people talk about polyphase decimation filter, I wonder
if it is more efficient than what I'm doing? What is the differrence?

thanks
mary

```
```mary1234567 wrote:

> I did a decimator FIR filter simply by doing the convolution only once
> every M' input sample.
> for example M=3:
>  feed x0,feed x1, feed x2, convolution, feed x3,feed x4, feed x5,
> convolution, feed x6,....
>
> Then I find many people talk about polyphase decimation filter, I wonder
> if it is more efficient than what I'm doing? What is the differrence?

IMO, there is only a conceptual difference or notational difference. From
the implementation point of view, both lead to identical complexity and
identical results (in the case of decimation). Polyphase comes handy as a
notational tool when systems get more complex than simple decimator.

--
Jani Huhtanen
Tampere University of Technology, Pori
```
```
mary1234567 wrote:

> I did a decimator FIR filter simply by doing the convolution only once
> every M' input sample.
> for example M=3:
>  feed x0,feed x1, feed x2, convolution, feed x3,feed x4, feed x5,
> convolution, feed x6,....
>
> Then I find many people talk about polyphase decimation filter, I wonder
> if it is more efficient than what I'm doing? What is the differrence?
>

There is no difference in your simple case.
The polyphase filter is handy when you need fractional decimation
ratios, and if the decimation is performed in the several stages.

DSP and Mixed Signal Design Consultant

http://www.abvolt.com
```
```Thanks for all the answers! Yes, I do have several decimate stages.(not
fractional)  I do every stage the same simple way. Will polyphase
decimator be more efficient then ?

Thanks!

```
```"mary1234567" <mjm0520@yahoo.com> wrote in message
news:NNCdnc5Mvoq9jnvenZ2dnUVZ_sednZ2d@giganews.com...
>I did a decimator FIR filter simply by doing the convolution only once
> every M' input sample.
> for example M=3:
> feed x0,feed x1, feed x2, convolution, feed x3,feed x4, feed x5,
> convolution, feed x6,....
>
> Then I find many people talk about polyphase decimation filter, I wonder
> if it is more efficient than what I'm doing? What is the differrence?

A polyphase filter simply recognizes that one need not multiply each
retained input sample by each filter coefficient for each output sample.
Most often the filter ends up looking like a number of filters in parallel
with inputs or outputs commutated at the sample rate.  This means that only
a subset of filter coefficients operate at each sample interval - and that's
efficient.  Then, if the idea is to decimate, some number of the outputs and
possibly those paths can be eliminated.

In my mind, polyphase is all about computational efficiency.  Otherwise why
bother mentioning it?  It doesn't change the underlying filters.

Fred

```
```"mary1234567" <mjm0520@yahoo.com> wrote in message
news:P8-dndQs_ePX6XreRVn-iQ@giganews.com...
> Thanks for all the answers! Yes, I do have several decimate stages.(not
> fractional)  I do every stage the same simple way. Will polyphase
> decimator be more efficient then ?

No. Since you only have simple decimation stages, you can do just as good
with what you have. It doesn't sound as cool as saying "I used a polyphase
filter" but it gets the job done and it essentially does the same thing a
polyphase works out to doing.

If you have sample rate changes where you have both interpolation and
decimation (say a rate change of 9/7), then a polyphase filter would be an
excellent choice.

Cheers

```
```mary1234567 wrote:
...
> Then I find many people talk about polyphase decimation filter, I wonder
> if it is more efficient than what I'm doing? What is the differrence?
...

You might want to look at dspGuru's "Multirate FAQ" at
http://dspguru.com/info/faqs/mrfaq.htm.  It covers a broad range of
issues related to decimation, interpolation, and resampling in a format
that's (hopefully) pretty practical and easy to understand.

=g2
--
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Grant R. Griffin
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