# Rational\_resampler vs pfb\_arb\_resampler filter design -- why such strange cut frequencies in both ca

**URL:** <https://www.ruby-forum.com/t/rational-resampler-vs-pfb-arb-resampler-filter-design-why-such-strange-cut-frequencies-in-both-ca/232697>\
**Category:** GNU Radio\
**Created:** [October 22, 2014, 11:40pm UTC](https://www.ruby-forum.com/t/rational-resampler-vs-pfb-arb-resampler-filter-design-why-such-strange-cut-frequencies-in-both-ca/232697 "2014-10-22T23:40:24Z")\
**Posts on this page:** 3\
**Page:** 1

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**Author:** ![addis\_a](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/a/c4cdca/32.png) [@addis\_a](https://www.ruby-forum.com/u/addis_a)\
**Post date:** [October 22, 2014, 11:40pm UTC](https://www.ruby-forum.com/t/rational-resampler-vs-pfb-arb-resampler-filter-design-why-such-strange-cut-frequencies-in-both-ca/232697/1 "2014-10-22T23:40:24Z")

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I’m looking at filter design procedures for rational\_resampler and  
pfb\_arb\_ resampler and see contradiction between them.

Lets assume downsample with rate 3/4 or 0.75. Lets source sample rate  
to be 10000 (so, target sample rate should be 7500), but, in fact, it  
is irrelevant.

rational\_resampler could be configured for this task with  
interpolation=3 and decimation=4. We’ll set fractional\_bw to “0.4” to  
match arb\_resampler “80%” multiplier. design\_filter() method in  
rational\_resample.py will create low-pass filter with:

gain = 3  
FS = 1  
transition center = 0.4/3 = 0,1(3) of 30000 = 4000 (!!!)  
transition width = 0.1

It doesn’t look resonable, as 4000 is more than 3750 which is Nyquist  
frequency for targer sampling rate.

Lets look at arbitrary resampler (pfb.py):

rate is \< 1. so it takes first branch:

gain = 32 (default number of filters)  
FS = 32 (WHY?!)  
transition center = 0.5 \* 0.75 \* 0.8 = 0.3 (And it should be in Hz!)  
transition width = 0.15

As you can see, parameters are rather different. But in this case  
filter should be roughly the same, because task is the same! We need  
to filter out all frequencies below 3750!

And both methods raise the questions. I could not say, that one of  
the methods looks good to me. Questions are:

(1) Why rational resampler doesn’t take decimation in account when  
calculates bandwidth? It design filter which will correctly reject all  
images in upsample, but looks like aliasing is possibly when effective  
ratio is less than 1, as only interpolation is used in bandwidth  
calculation and resulting filter “effectively” works at upsampled rate.

(2) Why arbitrary resampler set Fs to number of filters and AFTER  
that pass bandwidth numbers as normalized to 1, not to this Fs?! 0.3  
is perfectly good (may be slighly conservative, but Ok) transition  
band center, but in this case this 0.3 will be taken for FS=1, and  
here FS=32 (number of filters) is used, so it will be 32 times too low  
(!).

Are these two peculiarities two bugs, really, or I don’t understand  
something?

Yes, I’ve read harris’ book on multirating processing, and AFTER this  
book I got these questions.

* * *

Black Lion AKA Lev Serebryakov  
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**Author:** ![Lev\_Serebryakov](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/l/0ea827/32.png) [@Lev\_Serebryakov](https://www.ruby-forum.com/u/Lev_Serebryakov)\
**Post date:** [October 27, 2014, 6:06pm UTC](https://www.ruby-forum.com/t/rational-resampler-vs-pfb-arb-resampler-filter-design-why-such-strange-cut-frequencies-in-both-ca/232697/2 "2014-10-27T18:06:18Z")

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On 23.10.2014 01:39, Lev Serebryakov wrote:

> I’m looking at filter design procedures for rational\_resampler and  
> pfb\_arb\_ resampler and see contradiction between them.  
> So, no comments?

* * *

// Black Lion AKA Lev Serebryakov  
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<div class="post-metadata">

**Author:** ![Lev\_Serebryakov](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/l/0ea827/32.png) [@Lev\_Serebryakov](https://www.ruby-forum.com/u/Lev_Serebryakov)\
**Post date:** [October 28, 2014, 1:02pm UTC](https://www.ruby-forum.com/t/rational-resampler-vs-pfb-arb-resampler-filter-design-why-such-strange-cut-frequencies-in-both-ca/232697/3 "2014-10-28T13:02:36Z")

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On 23.10.2014 01:39, Lev Serebryakov wrote:

> (1) Why rational resampler doesn’t take decimation in account when  
> calculates bandwidth? It design filter which will correctly reject  
> all images in upsample, but looks like aliasing is possibly when  
> effective ratio is less than 1, as only interpolation is used in  
> bandwidth calculation and resulting filter “effectively” works at  
> upsampled rate.  
> Here I’m right, according to other thread.

> (2) Why arbitrary resampler set Fs to number of filters and AFTER  
> that pass bandwidth numbers as normalized to 1, not to this Fs?!  
> 0.3 is perfectly good (may be slighly conservative, but Ok)  
> transition band center, but in this case this 0.3 will be taken for  
> FS=1, and here FS=32 (number of filters) is used, so it will be 32  
> times too low (!).  
> And here I’mn wrong, and code is right, as filter effectively work  
> and “higher” frequency and all frequencies should be properly scaled.

* * *

// Black Lion AKA Lev Serebryakov  
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