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[Discuss-gnuradio] Definition of "radians per sample"

From: Daniele Nicolodi
Subject: [Discuss-gnuradio] Definition of "radians per sample"
Date: Wed, 25 Mar 2015 14:09:58 +0100
User-agent: Mozilla/5.0 (Macintosh; Intel Mac OS X 10.9; rv:31.0) Gecko/20100101 Thunderbird/31.5.0


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,

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