# Definition of "radians per sample"

**URL:** <https://www.ruby-forum.com/t/definition-of-radians-per-sample/234737>\
**Category:** GNU Radio\
**Created:** [March 25, 2015, 2:11pm UTC](https://www.ruby-forum.com/t/definition-of-radians-per-sample/234737 "2015-03-25T14:11:39Z")\
**Posts on this page:** 2\
**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:** [March 25, 2015, 2:11pm UTC](https://www.ruby-forum.com/t/definition-of-radians-per-sample/234737/1 "2015-03-25T14:11:39Z")

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Hello,

the documentation for the PLL blocks in GNURadio says: “All settings  
max\_freq and min\_freq are in terms of radians per sample, NOT HERTZ.”

Therefore I thought that to specify a bandwidth `bw` it would have to  
converted from natural frequency units (Hz) into radians per sample with  
something like:

bw\_rad\_per\_sample = bw \* 2\*pi / sampl\_rate

where `sampl_rate` is of course the sampling rate in Hz.

However, looking at the PSD of the input and outputs to the PLL blocks,  
it looks like my understanding is wrong and that the bandwidth should be  
computed as

bw\_rad\_per\_sample = bw \* pi / sampl\_rate

which differs from the former by a factor of 2.

Is the documentation right, and my understanding of it wrong, or the  
documentation is wrong? In the former case, I think it would be better  
to clarify it a bit.

Thanks! Cheers,  
Daniele

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**Author:** ![Daniele\_N](https://www.ruby-forum.com/letter_avatar_proxy/v4/letter/d/74df32/32.png) [@Daniele\_N](https://www.ruby-forum.com/u/Daniele_N)\
**Post date:** [March 27, 2015, 2:59am UTC](https://www.ruby-forum.com/t/definition-of-radians-per-sample/234737/2 "2015-03-27T02:59:05Z")

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Hello Mohamed,

I didn’t consider the difference between baseband and passband bw, but  
isn’t the difference by a factor two going in the wrong direction here?

If I assume that the PLL blocks want the bw defined as passband, when I  
get the signal out of the PLL blocks at baseband, I should see a bw that  
is half of the one I specified at passband, not twice it.

If I assume that the PLL blocks want the bw defined as baseband, I  
should see no difference in bw.

I’m still puzzled.

Cheers,  
Daniele