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I have a simple, but interesting question for you. I have to compute the RMS (root mean square or standard deviation) value of a time signal which represents in my case a velocity mesasurement over time, of course sampled an stored in a computer. In your opinion, does the sampling frequency have a strong impact on the RMS value or it is just the TOTAL number of samples that matters the most? Can you please, if possible, refer to some books where this topic is dealt with?

Thanks a lot, I'm looking forward to reading your answers.

Bye

E.

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If the sampling rate meets the nyquist criteria (sampling rate more than twice the highest frequency in the signal) then it won't be a factor in the accuracy of the RMS value.

Since you are measuring velocities the nyquist criteria could be a problem if you don't know the frequencies involved. The frequencies would be related to the acceleration - higher acceleration means higher frequencies. I don't know how to tell you to determine the needed sampling rate give the expected acceleration.

If you can't determine the highest frequency (or are limited in your sampling frequency,) then you might run your sampling at the highest available rate, but filter the analog signal with a lowpass with a cutoff frequency lower than half of the sampling rate. This will avoid the problems that arise when sampling a fast signal with a too slow sampling rate, at the expense of throwing away information if the sampling rate really is too slow.

The number of samples only comes into it when trying to calculate the RMS value of a repeating signal, line a sine wave. In that case you have to make sure to get a least one full cycle of the lowest frequency. More could help make up for inaccuracies in the measurement or reduce some of the noise. In this case, the longer sampling period averages out any measurement errors and noise.

Summary: Make sure that your sampling is fast enough, that the samples are evenly spaced, and that you (obviously) have all the samples for the period of interest.

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  • $\begingroup$ Thank you very much for you answer, what you said makes sense to me! $\endgroup$ – EmThorns Oct 28 '14 at 19:59
  • $\begingroup$ I am currently looking into an issue in this area and the data so far, shows that RMS changes when resampling the signal. I use the RMS of an impulse response to scale the convolution signal produced and when the IR is resampled to longer SampleFrequency I get a lower than the regular RMS value. The opposite is also true - when I resample the IR to lower frequency, I get a larger RMS value. A working solution for me is to get RMS on the original SampleFrequency and then divide that with newFs/origFs. $\endgroup$ – Nikolay Tsenkov Apr 30 '17 at 15:59

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