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## Re: [Discuss-gnuradio] RMS value of a signal changes with PAPR

 From: Marcus Müller Subject: Re: [Discuss-gnuradio] RMS value of a signal changes with PAPR Date: Mon, 13 Apr 2015 17:45:33 +0200 User-agent: Mozilla/5.0 (X11; Linux x86_64; rv:31.0) Gecko/20100101 Thunderbird/31.6.0

```Hi Tomaž,

this points to your signal generator simply defining "the same power"
differently for modulation, noise and a sine wave.

Generally, things get a bit hairy as soon as you try to compare powers.
per frequency step.
When observing a narrowband signal, you might, for example, set that
bandwidth to 200kHz. Now, your sine will have exactly the same power in
that window as if you observerd it with a 2MHz bandpass. For pseudowhite
noise, however, measured power will be linear to observed bandwidth --
because "white" defines the power spectral density to be constant, so
your 2MHz filter will see ten times the noise power of your 2kHz filter.

You already take care of that, by using a filter of your own -- however,
I can't tell from your blog post about the spectral properties of your
filter. Typically, when designing a filter, you have to make the choice
(at a fixed length) between sharp transition from pass- to stopband, and
low integral power of stopband "leakage". The typical way of determining
the total power that passes through a filter is observing its response
to white noise -- which is exactly what you're doing. So my blind guess
would be that your spectrum analyzer's filters are way sharper than your

You could play with different filter designs, longer filters, and even
cascading of a well-suppressing and a sharp-edgy filter, decimating as
far as each step allows. You should then look at the spectral shape.
Luckily, Parseval's theorem says that the energy of the Fourier
transform is proportional to the energy in time domain, so just looking
at the sum of squares of taps will give you a value that's proportional
to the total power that your filter lets through.

Regarding modulated signal: I'd assume that your signal generator uses
some pulse shape -- maybe a root-raised cosine, or so, to convert the
individual symbols to baseband signals. These filters might or might not
actually be truely represented by the "constant power" setting, and just
as noise, they have a non-zero bandwidth. Depending on your filtering,
you might see more or less of the complete spectral shape of your pulse
(or the symbol rate spectral repetitions).

I hope I guessed in the right direction,
best regards,
Marcus

[1] by default, some daughterboards/USRPs have adjustable analog bandwidth

On 04/13/2015 05:18 PM, Tomaž Šolc wrote:
> Dear all,
>
> I'm calculating the RMS value of a signal with the following setup
>
> RF vector signal generator -> USRP/rtl-sdr/... -> "RMS" block in GRC.
>
> Please bear with me - I'm not interested in the exact (absolute) voltage
> level.
>
>
> What I can't explain is why the calculated RMS value consistently shows
> a higher value when the signal is modulated (e.g. has a higher
> peak/average power ratio) compared to CW (unmodulated sine wave)
>
> For instance, RMS value shown in GRC for band-limited Gaussian noise is
> always around 2.5 dB _higher_ than RMS of CW of equivalent power
> (equivalent power according to the generator level setting and a
> spectrum analyzer with a power meter function). Similarly, 100% AM
> modulated signal shows around 1.3 dB _higher_ RMS.
>
> This effect appears with a USRP, rtl-sdr dongle as well as some custom
> hardware, so it doesn't seem to be something device-specific. Also, all
> hardware effects on the receiver side I can imagine result in _lower_
> gain for modulated signals. If anything, I would expect to see a _lower_
> RMS when turning on the modulation.
>
> Some more details are in this blog post:
>
>
> Any ideas would be welcome. At this point I have a feeling I'm missing
> something obvious here...
>
> Thanks,
> Tomaž
>
> _______________________________________________