# High pass polyphase filter

Started by June 30, 2009
```Hi all,

I'm trying to design an high pass polyphase filter.

The approach is to take the 5 tap high pass FIR,
oversample it by a factor N (usually 128 or 256), then
subsample it again into the different phases.

The oversampling was done by polynomial interpolation
I mean, the two methods were tried, not altogether.

In both cases, the results are disappointing.

Phase 0 is, of course, correct, but as soon as different
phases are chosen, the frequency response become crazy.
Basically the attenuation increases in the high pass
band and it reaches zero to certain phases.

Now, I was wondering, could it be there is a theoretical
reason why it does not seem possible to design an high
pass polyphase filter or the design methods are wrong?
Methods, which, by the way, work fine with low pass
polyphase filter design.

Any idea? Suggestions?

Thanks,

bye,

--

piergiorgio
```
```Piergiorgio Sartor wrote:

> I'm trying to design an high pass polyphase filter.

Design a lowpass filter with complementary bandedge
wc' = pi - wc and modulate the IR with the sequence (-1)^n.

> The approach is to take the 5 tap high pass FIR,
> oversample it by a factor N (usually 128 or 256), then
> subsample it again into the different phases.
>
> The oversampling was done by polynomial interpolation
> and by zero-padding and low-pass.
> I mean, the two methods were tried, not altogether.

> Phase 0 is, of course, correct, but as soon as different
> phases are chosen, the frequency response become crazy.
> Basically the attenuation increases in the high pass
> band and it reaches zero to certain phases.

Highpass FIR coefficients alternate in sign, so the point-to-point
variation is large and you get the well-known phenomenon that the
interpolating polynomial goes through the roof between sample points.

Martin

--
Quidquid latine scriptum est, altum videtur.
```
```On Jun 30, 11:18&#2013266080;am, Piergiorgio Sartor
<piergiorgio.sartor.this.should.not.be.u...@nexgo.REMOVETHIS.de>
wrote:
> Hi all,
>
> I'm trying to design an high pass polyphase filter.
>
> The approach is to take the 5 tap high pass FIR,
> oversample it by a factor N (usually 128 or 256), then
> subsample it again into the different phases.
>
> The oversampling was done by polynomial interpolation
> and by zero-padding and low-pass.
> I mean, the two methods were tried, not altogether.
>
> In both cases, the results are disappointing.
>
> Phase 0 is, of course, correct, but as soon as different
> phases are chosen, the frequency response become crazy.
> Basically the attenuation increases in the high pass
> band and it reaches zero to certain phases.
>
> Now, I was wondering, could it be there is a theoretical
> reason why it does not seem possible to design an high
> pass polyphase filter or the design methods are wrong?
> Methods, which, by the way, work fine with low pass
> polyphase filter design.
>
> Any idea? Suggestions?
>
> Thanks,
>
> bye,
>
> --
>
> piergiorgio

Piergiorgio,

A polyphase filter structure is simply a zero stuff interpolator
followed by a low pass filter and then a decimation block.  When you
interpolate with zero stuffing it creates images.  If you high pass
filter you will not get rid of all the replacated images.  The
decimation stage will alias strange artifacts back into your passband.

You could try designing a low pass filter polyphase and then just
simply using a frequency translate (multiply by sin/cos) the input,
filter and then translate back.  It may be possible to integrate the
two processes into the same polyphase structure.

Michael Kreeger

http://kreegerresearch.com/
```
```Piergiorgio Sartor wrote:
> Hi all,
>
> I'm trying to design an high pass polyphase filter.
>
> The approach is to take the 5 tap high pass FIR,
> oversample it by a factor N (usually 128 or 256), then
> subsample it again into the different phases.
>
> The oversampling was done by polynomial interpolation
> and by zero-padding and low-pass.
> I mean, the two methods were tried, not altogether.
>
> In both cases, the results are disappointing.
>
> Phase 0 is, of course, correct, but as soon as different
> phases are chosen, the frequency response become crazy.
> Basically the attenuation increases in the high pass
> band and it reaches zero to certain phases.
>
> Now, I was wondering, could it be there is a theoretical
> reason why it does not seem possible to design an high
> pass polyphase filter or the design methods are wrong?
> Methods, which, by the way, work fine with low pass
> polyphase filter design.

In theory and often in practice, a polyphase filter is no different than a
filter that can be split up into handy chunks.  Usually this is because the
filter has a sparse time structure.  The simplest is as a half-band filter
where the coefficients are alternately zero (except the center coefficient).
Then, more contiguous zeros can be added so that the filter is zero for more
and more samples between each of the nonzero ones.  Each regularly occuring
zero provides the opportunity for a "phase" in a polyphase structure.  (Note
I say "structure" and not "filter" because there should be no difference in
either "filter").  The same criteria could be applied to the data where
oversampling causes multiples of periodic zeros between the nonzero samples.

I'm more than a little confused by your objectives and approach:

If you start with a 5-coefficient FIR and then modify it, it appears you're
doing filter design.  Why not just do it directly?

Just to be sure:  You oversample the FIR filter (in time) and then you
interpolate it (in time).  Is that it?  That seems a pretty inaccurate way
to get a long filter - using a short filter as a prototype.

*****

What are you trying to do?  I mean in the context of dealing with a signal.
What does the signal look like and what do you want to do with it?  Where
does the polyphase notion come into the picture?  Once more: "polyphase" is
a trick that you do to reduce computations when either the filter or the
data have certain nice properties.  How is it that those properties exist in

Fred

```
```On 07/03/2009 12:50 AM, Fred Marshall wrote:

> If you start with a 5-coefficient FIR and then modify it, it appears you're
> doing filter design.  Why not just do it directly?

The 5-taps FIR is "given", so to speak, so I cannot invent
it and I want to have the phase zero identical to this one.

> Just to be sure:  You oversample the FIR filter (in time) and then you
> interpolate it (in time).  Is that it?  That seems a pretty inaccurate way
> to get a long filter - using a short filter as a prototype.

Well, that's why I'm asking: what is the correct way?

> What are you trying to do?  I mean in the context of dealing with a signal.

As I said, I need an high-pass filter capable of phase shifting
the input signal.
Normally, with low-pass or even band-pass, this was never a
problem, also because there was more freedom in the design.

Now, the constrains is the given 5-taps high-pass filter.

> What does the signal look like and what do you want to do with it?  Where

The signal looks like anything, is non-stationary, quite
self-correlated, maybe with some white noise, nothing, I
think, with special properties, quite dull :-)...

> does the polyphase notion come into the picture?  Once more: "polyphase" is

As I said, I need to high-pass, but I need output values
which are not at integer position and I want to do it in
a single step, i.e. no high-pass and then interpolation
(which would be, in the end, the same as interpolate the
filter and then use it).

> a trick that you do to reduce computations when either the filter or the
> data have certain nice properties.  How is it that those properties exist in

The only thing I can think of is that the concept of
"high-pass" and those properties are mutually exclusive.

If not, the input signal should not play a role, here.

Thanks again,

bye,

--

piergiorgio
```