Doubts in 1/f noise- DC problem

As we all know 1/f noise has more value near the DC. So obviously if you average the signal for a long time you are probably going to get some high value (at least little bit high). Does this mean that when you see a signal its DC (which is obtained by adding all values) is constantly increasing as the time progresses. This should mean that you don't have a stationary process (or in other words constant mean). I tried generating a 1/f noise using MATLAB (got the correct spectrum for 1/f noise) and I noticed this- When I summed all the data values for a some range (starting from 0) I got a non zero value. After this I increased the range and I got some other non-zero value (more than what I got before). So it should mean that its not a stationary process (and obviously as you keep on increasing the range the value keeps on increasing which indicates that at DC you should get infinity right?).

Assume a constant DC voltage + noise. Then an averaged voltage measurement is an unbiased estimator for the DC voltage. By increasing the measurement time respectively number of averaged samples, the uncertainty will be reduced. Which value do you see constanly rising?

Correction. I tried once again and I got somewhat different result. But what I can assure you is that the sum of all samples ( I took 10 Meg samples) was about 500 (which is very high). What I couldn't understand in this 1/f noise is this- Even though the signal seems to be swinging around 0, I am getting a very high DC value after summing everything. Can you help me in understanding this 1/f noise further?

Also I have one more doubt- I see people saying observing something for one day in 1/f noise. That means adding all the samples for one day right?

Also I more doubt- To find out the 1/f noise around 10^-3 Hz they actually say we have to observe for 1000 s. Do they mean adding all the samples for 1000 s?

Thanks in advance.

1/f noise is AC. It has been observed that you might consider the slow microvolt DC drift with time of an op amp due to very low frequency 1/f noise. Otherwise the average value of 1/f noise is zero. Thus for measurement, you take the samples and then average them by adding them together (with polarity sign) and dividing that by the number of samples.

But what I can assure you is that the sum of all samples ( I took 10 Meg samples) was about 500 (which is very high).

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The average value is 500/10e6, that's not very high.... Seriously speaking, those numbers are meaningless unless we know about the measurement problem. The question is however, if you calculate the average value correctly.

To find out the 1/f noise around 10-3 Hz they actually say we have to observe for 1000 s. Do they mean adding all the samples for 1000 s?

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Calulation of the average value, see above. "Noise around 10-3 Hz" is a matter of spectral analysis.

There are only few electrical problems where it would be meaningful to determine noise density below 0.1 Hz. The noise corner frequency is typically much higher and the noise density can be estimated by extrapolating the 1/f characteristic.

Hi everybody! Virtually everything said here is true, but you don't answer the original question:

SherlockBenedict said:

So it should mean that its not a stationary process (and obviously as you keep on increasing the range the value keeps on increasing which indicates that at DC you should get infinity right?).

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Flicker noise is indeed not stationary. As you can see in Fig. 4 of the Flicker Noise Chapter of the CRC Book Circuits at the Nanoscale: Communications, Imaging, and Sensing (http://schmid-werren.ch/hanspeter/publications/2008crcbook.pdf), the RMS of a flicker noise process increases with time.

For an intuitive understanding of WHY flicker noise is not stationary, I can recommend http://schmid-werren.ch/hanspeter/publications/2007casmag.pdf .

In theory you will go to infinity; not in practice, though. Flicker noise comes from memory effects, and every physical system has some lowest memory time constant T. Below f=1/T, the noise does not increase anymore. For MOSFETs, that T is rather larger than you'd believe, estimated to be in the region of weeks (!) for submicron processes.

Slainte!
H

Virtually everything said here is true, but you don't answer the original question.

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Yes, thank you clarifying the point. I must admit that I was looking at the post more from a practical measurement perspective, somehow blanking out the theoretical problem. I stumbled upon the "constantly increasing as the time progresses" in the original post which isn't true at all. But as you claimed correctly, the variance increases by a certain amount for each doubling of the measurement interval. So the error of a 1/f noise affected measurement increases in time, but not constantly.

In the world of practical measurement, you have long time drift and limited calibration validity representing similar effects. I'm not sure, if the aging processes that are apparently assumed to have a 1/f statistic actually follow it strictly or possibly behave better. But as far as I understand, at least MOSFET Vth seems to have a true 1/f characteristic for very longt time periods.

The average value is 500/10e6, that's not very high.... Seriously speaking, those numbers are meaningless unless we know about the measurement problem. The question is however, if you calculate the average value correctly

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Ya ya. I forgot to divide. Anyway it is non-zero unlike awgn. As hanspi suggested I noticed this also- the mean kept on varying when I increased the number of samples for averaging. I read somewhere that 1/f noise is present everywhere. It looks as if it is related with the aging of the devices, which would result in changes in the characteristic of the device. Am I correct?

I read somewhere that 1/f noise is present everywhere.

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It seems so. But I would be still careful to conclude the exact behaviour of real systems from the 1/f noise model. In theory, the average doesn't converge for t -> ∞, practically the average is finite during the lifetime of the system (and even our known universe). And even more: We don't know, if the mean value might converge for large t values for a real system.

As another point, I reviewed my Signal Theory text books and from it's viewpoint, 1/f noise seems to be still a quasistationary process (as regular white noise too), because the spectrum would be expected invariant to time shifts. As far as I understand, this invariance is a prerequisite of the 1/f noise generator model.

You are raising a very difficult point here. 1/f noise is only quasistationary if the time scale you are looking at is relatively short compared to the time that has passed since the flickering system has been switched on. Right after switch-on, it is not even quasi-stationary. This also has implications, e.g., for using correlated double sampling in image sensors; if you do that wrong, you increase 1/f noise instead of cancelling it.

This non-stationarity of flicker noise has been shown nicely, by measurement, by Arnoud van der Wel in https://ieeexplore.ieee.org/xpl/articleDetails.jsp?tp=&arnumber=4114769

Slainte!
H