Definition of "radians per sample"


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,

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.