# Resampling Polyphase Fir Filter

Started by October 23, 2015
```On 10/23/15 2:53 PM, kaz wrote:

>>
>> how to find the 2 sided bandwidth  stopband frequency and the sampling
>> rate AND weigth of the inner filter from the given analysis filter.
>> for example, the input sample rate is 24 .if we do 12 to 1 downsampling
>> and then upsampling of 1 to 12 .the output sample rate will become 24/12
> 2. but how do we find the transition band.i tried using sampling theorem.
>> nyquist rate =2sided band + transition bandwidth. Asuming the 2 sided
>> banwidth same as the analysis filter and nyquist rate equal to 2. Is it
>> the right way to do it.
>
> upsample by 12 then downsample by 12. Why? what do do in between?
>

maybe something non-linear (with power terms up to x^23) maybe with
anti-alias filtering.

--

r b-j                  rbj@audioimagination.com

"Imagination is more important than knowledge."

```
```>On 23.10.15 22:37, Piergiorgio Sartor wrote:
>> On 2015-10-23 21:24, angeleye wrote:
>> [...]
>>> Down Sample to Reduce Sample Rate in Proportion to Bandwidth
Reduction
>>
>> You wrote "12 to 1 downsampling".
>> This does not need polyphase filter.
>> The upsampling 1 to 12 does not need either.
>>
>> Other, I do not know... :-)
>>
>> bye,
>
>
>It seems to me that his professor has some solution in his mind,
>and attempting to fish it out using a weirdly set up problem.
>
>--
>
>-TV
It is still not clear to me . I have to implement M to 1 polyphase
partition ad downsampling of low pass filter and then cascade M to 1 and 1
to M polyphase fir filter maintaining the constant sample rate.

---------------------------------------
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```
```On 2015-10-24 06:13, angeleye wrote:
[...]
> It is still not clear to me . I have to implement M to 1 polyphase
> partition ad downsampling of low pass filter and then cascade M to 1 and 1
> to M polyphase fir filter maintaining the constant sample rate.

It seems it is not clear to many people too...

An M to 1 down-sampling followed by a 1 to M up-sampling
is nothing more than a low pass filter with a cut off of
1/M of the bandwidth.

So, since M is a (small) integer, this is no problem to
implement as normal low pass filter.
Unless, of course, there is more I did not get.

I suggest to re-read the assignment carefully and relate
each *detail* to what was explained during the lessons.

bye,

--

piergiorgio
```
```>On 2015-10-24 06:13, angeleye wrote:
>[...]
>> It is still not clear to me . I have to implement M to 1 polyphase
>> partition ad downsampling of low pass filter and then cascade M to 1
and
>1
>> to M polyphase fir filter maintaining the constant sample rate.
>
>It seems it is not clear to many people too...
>
>An M to 1 down-sampling followed by a 1 to M up-sampling
>is nothing more than a low pass filter with a cut off of
>1/M of the bandwidth.
>
>So, since M is a (small) integer, this is no problem to
>implement as normal low pass filter.
>Unless, of course, there is more I did not get.
>
>I suggest to re-read the assignment carefully and relate
>each *detail* to what was explained during the lessons.
>
>bye,
>
>--
>
>piergiorgio

I am not clear either. One scenario is that if I want to introduce 1/12
fractional delay then I will conceptually upsample by 12 and then
downsample by 12 choosing one phase out of 12.

In such case I don't need to implement any true full
upsampling/downsampling but rather just choose the relevant polyphase out
of 12.

Kaz

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```
```"angeleye" <109705@DSPRelated> wrote in
news:PvSdncvfO54emLbLnZ2dnUU7-KGdnZ2d@giganews.com:

> It is still not clear to me . I have to implement M to 1 polyphase
> partition ad downsampling of low pass filter and then cascade M to 1
> and 1 to M polyphase fir filter maintaining the constant sample rate.
>
>
> ---------------------------------------
> Posted through http://www.DSPRelated.com
>

Chech this PDF.

https://wireless.vt.edu/symposium/2011/tutorials/Session%20A3_Part%203
_Multirate_DSP_Wireless_2011.pdf

Mass

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```
```>"angeleye" <109705@DSPRelated> wrote in
>news:PvSdncvfO54emLbLnZ2dnUU7-KGdnZ2d@giganews.com:
>
>
>> It is still not clear to me . I have to implement M to 1 polyphase
>> partition ad downsampling of low pass filter and then cascade M to 1
>> and 1 to M polyphase fir filter maintaining the constant sample rate.
>>
>>
>> ---------------------------------------
>> Posted through http://www.DSPRelated.com
>>
>
>Chech this PDF.
>
>https://wireless.vt.edu/symposium/2011/tutorials/Session%20A3_Part%203
>_Multirate_DSP_Wireless_2011.pdf
>
>
>
>Mass
>
>
>
>--- news://freenews.netfront.net/ - complaints: news@netfront.net ---
hi
I am not able to open this link ..it shows "The requested URL
server."

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```
```>>"angeleye" <109705@DSPRelated> wrote in
>>news:PvSdncvfO54emLbLnZ2dnUU7-KGdnZ2d@giganews.com:
>>
>>
>>> It is still not clear to me . I have to implement M to 1 polyphase
>>> partition ad downsampling of low pass filter and then cascade M to 1
>>> and 1 to M polyphase fir filter maintaining the constant sample rate.
>>>
>>>
>>> ---------------------------------------
>>> Posted through http://www.DSPRelated.com
>>>
>>
>>Chech this PDF.
>>
>>https://wireless.vt.edu/symposium/2011/tutorials/Session%20A3_Part%203
>>_Multirate_DSP_Wireless_2011.pdf
>>
>>
>>
>>Mass
>>
>>
>>
>>--- news://freenews.netfront.net/ - complaints: news@netfront.net ---
>hi
>I am not able to open this link ..it shows "The requested URL
>server."
>
>---------------------------------------
>Posted through http://www.DSPRelated.com

---------------------------------------
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```
```>hello,
>i am trying to do 12 to 1 downsampling and 1 to 12 upsampling with
>polyphase fir filter, I wanted to know how to design the inner filter.
>suppose passband frquency is 0.5, stopband freq is 0.75. input sample
rate
>is 24 ,inband ripple is 0.1 and outband attenuation is 80db.and it is 12
>path filter with filter length is equal to 348 .each path is followed by
>29 taps.how to design the inner filter such that it meets the
>specification of the synthesis filter..

According to Fliege, Multirate Digital Signal Processing, p. 115-117,
the decimation and interpolation filters are the same, have a passband
ripple of 0.1/3 each, and the stopbands start at (24/12)-0.75 = 1.25.
For the kernel filter (your inner filter) the passband ripple is
0.1/3, the attenuation is 80 dB, and the stopband is 0.75, with a
sampling rate for that filter of 2. Hope this helps. The polyphase filters
will be the interpolation and decimation filter implementations.

This implementation of a lowpass filter (filter, decimate, filter,
upsample, filter) sometimes reduces the overall computing complexity
(filter operations per second) of a single filter with passband 0.5,
stopband 0.75, sampling rate 24.

---------------------------------------
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```
```>hello,
>i am trying to do 12 to 1 downsampling and 1 to 12 upsampling with
>polyphase fir filter, I wanted to know how to design the inner filter.
>suppose passband frquency is 0.5, stopband freq is 0.75. input sample
rate
>is 24 ,inband ripple is 0.1 and outband attenuation is 80db.and it is 12
>path filter with filter length is equal to 348 .each path is followed by
>29 taps.how to design the inner filter such that it meets the
>specification of the synthesis filter..
>
>
>
>---------------------------------------
>Posted through http://www.DSPRelated.com

This problem is discussed in Fliege, Multirate Digital Signal Processing,
p. 115-118, in connection with the design of lowpass filters with low
frequency cutoff. The technique involves a decimation filter, a decimator,
a kernel filter, an interpolator and an interpolation filter. The
decimation and interpolation filters may be economically realized with a
polyphase structure. With the values quoted, the decimation and
interpolation filters at rate 24 have a passband edge at 0.5, and a
stopband starting at 24/12-0.75=1.25. The kernel filter (i.e. the inner
filter) has a passband edge at 0.5, and a stopband starting at 0.75 as
stated. The filters all have stopband ripple quoted (80 dB, or 0.0001),
but the passband ripple is conservatively set at 0.1/3=0.03.

---------------------------------------
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```
```>>hello,
>>i am trying to do 12 to 1 downsampling and 1 to 12 upsampling with
>>polyphase fir filter, I wanted to know how to design the inner filter.
>>suppose passband frquency is 0.5, stopband freq is 0.75. input sample
>rate
>>is 24 ,inband ripple is 0.1 and outband attenuation is 80db.and it is
12
>>path filter with filter length is equal to 348 .each path is followed
by
>>29 taps.how to design the inner filter such that it meets the
>>specification of the synthesis filter..
>
>
>According to Fliege, Multirate Digital Signal Processing, p. 115-117,
>the decimation and interpolation filters are the same, have a passband
>ripple of 0.1/3 each, and the stopbands start at (24/12)-0.75 = 1.25.
>For the kernel filter (your inner filter) the passband ripple is
>0.1/3, the attenuation is 80 dB, and the stopband is 0.75, with a
>sampling rate for that filter of 2. Hope this helps. The polyphase
filters
>will be the interpolation and decimation filter implementations.
>
>This implementation of a lowpass filter (filter, decimate, filter,
>upsample, filter) sometimes reduces the overall computing complexity
>(filter operations per second) of a single filter with passband 0.5,
>stopband 0.75, sampling rate 24.
>
>
>---------------------------------------
>Posted through http://www.DSPRelated.com

This makes sense now, though OP was less clear. So you decimate from 24 to
2 (using suitable filter to prevent aliasing), do the filtering now in
this slow domain hence cutoff ratio increases by 12) then upsample back.

I am not sure why would it be any better than single LPF but that depends.
Surely this solution with three filter modules, suits software dsp but
not hard platforms like fpga.

Kaz
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```