## Getting Standard Deviation from Noise Density

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Hello, I've seen in a bunch of datasheets a spectral noise density figure, expressed in Units/sqrt(Hz).

In my case, I'm trying to assess the measurement error in an accelerometer, where noise is expressed in micro-g/sqrt(Hz). I was wondering how to convert from noise density to standard deviation in measurement values. I do remember hearing about flicker noise in RF classes, I have a feeling it should be a similar process as to getting the phase noise of an oscillator.

Any ideas?

My experience suggests standard deviation is a way to calculate RMS. You have to have an understanding of mathematics to understand how beautiful that is in working with uC.

Here is a a good youtube from ADI on how to convert SD to RMS.

It all starts with a mental vision.

KitCarlson wrote:
Here is a a good youtube from ADI on how to convert SD to RMS.

+1 Video :)

BUT accelerometers are special beasts. Whist the Noise density is a good approximation for the white noise component, accelerometers have significant long-term correlated noise.

If the noise was purely white, if you averaged for longer and longer periods, the standard deviation will reduce forever.

After some averaging time, the standard deviation will stay flat with longer averaging times (this is "flicker noise"). Even longer averaging times, and the standard deviation will increase because of a random walk component.

(In reality, at some time, there will be some limit, but there is no real analytical use for averaging over that really long period!)

If you know how to do an Allan Variance chart from Oscillators, then this technique is directly applicable to inertial sensors - specific points on the chart are used to characterize (good quality) inertial sensors in the relevant IEEE standard.

-- Damien

And my experience of using standard deviation involved synchronous sampling over a complete cycle of the fundamental. It may not apply to accelerometer signal at all.

Damien is correct.

It all starts with a mental vision.