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I have an ADC sampling a downconverted RF signal at fs. I obtain N=2^15 samples of the RF input signal "fcarrier + fs/10".

The more I average, the more the entire noise floor shifts down (as expected, 10dB/dec) but also the phase noise skirt. I can average down to 100dB SNR (I didn't wait longer). For 1000 averages, the (zoomed) spectrum looks like this:

enter image description here

The phase noise skirt just moved down by 30dB as compared to the non-averaged version. This suggests I can average the phase noise out. But I would not expect it to be averaged out. According to http://www.bitsofbits.com/2015/07/07/signal-jitter-and-averaging/, the signal should be a cosine convolved with an exponential ("signal-leakage like") after infinite averages.

  • Can phase noise be reduced?
  • If yes, does can it be averaged out same as white noise? (This is what I observe above).
  • How does this fit into the link posted above?
  • Does it depend on the input signal? (sinusoid vs wideband)?
divB
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  • What sort of equipment gives enough resolution to read 4.761904761904762 MHz with that level of precision? – Transistor Jul 10 '18 at 22:32
  • As an engineer, numbers like 4.761904761904762 make me chuckle. – evildemonic Jul 10 '18 at 22:34
  • It just does not matter. Then no numbers. Numbers removed. – divB Jul 10 '18 at 22:37
  • @Transistor Answer: An extremely picky filter with the highest frigging Q-factor you've ever seen. Float value needs to be more specific. –  Jul 10 '18 at 23:08
  • If you have random noise, doesn’t an average of 2 = -3dB and 1000= -30dB in noise? – Tony Stewart EE75 Jul 11 '18 at 00:30
  • Yes, do I contractdict myself here? – divB Jul 11 '18 at 00:48
  • Be careful: averaging the noise also averages the signal, so beware of the resulting cutoff frequency. If it's a simple moving average, of the type `(a[0]+a[1]+...+a[N-1])/N` then it's a simple `sinc()`-like spectrum. – a concerned citizen Jul 11 '18 at 09:09
  • That makes sense but I should mention that I use "real" averaging: I obtain 10000 traces of the same signal, align them and then average them. I will add this to my question – divB Jul 12 '18 at 02:50
  • @KingDuken yes such as a crystal, loosely coupled to the input RF signal. Or a VCXO that gets fine-tuned to the center frequency using a PLL :-) The PLL filter defines "agility" of the lock / phase noise filter response. Oh wait - that's all much too analog, is it... Why not just phase-demodulate what you have, and filter the demodulated phase signal? – frr Jul 15 '18 at 05:34
  • Put another way, why not just perform an FFT over a time scale that fits your desired "phase demodulation bandwidth", and pick the tallest line? Or 2-3 tallest lines and *maybe* interpolate, if that makes any sense... The tallest line in the FFT spectrum is your "best fit" of the signal to an ideal sine wave. Sine+cosine in quadrature actually. Done in pure digital domain. By discarding all the other "minor" lines in the spectrum, you are discarding residuals. Modulo some windowing envelope, modulo the stability of your sampling clock, as analogsystemsrf has pointed out... – frr Jul 15 '18 at 06:00
  • It is an interesting question. I was under the same impression as you, that phase jitter convolves the ADC signal and shouldnt decrease... Why would ultra low jitter clocks be otherwise so paramount in fast ADCs ? I might do some more research and post an answer if I find something. Also maybe this could be answered better in DSP SE. – tobalt Apr 24 '21 at 10:42

1 Answers1

-1

Let us model additive noise, atop a sinusoidal carrier, as 2 small noise sources in quadrature.

We have this vector diagram

schematic

simulate this circuit – Schematic created using CircuitLab

The inphase noise is AM: amplitude modulation noise.

The quadrature noise is PM: phase modulation, or phase noise or jitter.

Is there any specific reason why more samples, averaged together, would not produce a lower standard deviation?

By the way, what is the ADC/sampling_clock phase noise spectrum?

=====================================================

Oct 31, 2020

Ahem. Phase is indeed additive.

Take a clean (clean enough) sinsoid, and sum with random noise.

The Time Jitter (phase noise, by another computation) is

Tj = Vnoise / SlewRate

and you can convert from Time Jitter to Phase noise, by recognizing the

PERIOD OF THE CARRIER versus the 1-sigma (RMS) of the computed Tj.

analogsystemsrf
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    This answer does not really help me yet and does not answer the question (IMO) but maybe I don't understand it yet. There is oscillator noise (consisting on amp.&phase noise) but phase noise is by definition phase only (and let's not assume I/Q for simplicity but only consider one channel). As I hinted in my question, PN is not additive but multiplicative, hence I don't expect averaging to work. Furthermore, does it make a difference if the signal is purely sinusoidal or a complex modulated signal? – divB Aug 07 '18 at 07:53
  • If you show the noise as a centroid around the tip this would be clearer. – Scott Seidman Jun 22 '19 at 16:34
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    Your first argument, I find indeed a little off the point, as noone doubts that random noise will average away as expeced. Your second argument however is logical. In fact, this is how I simulate the effect of jitter on noise spectra lol. But also another well known argument is: the phase noise spectrum convolves the signal spectrum. So I have the feeling that these two arguments contradict. Is the resolution here, that the phase noise spectrum itself drops in power the longer the portion of analysed waveform ? – tobalt Apr 24 '21 at 10:47