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I have a raw EEG signal of length 2,50,000 samples. I band passed it from 0.05-10Hz (sampling frequency=500). Then I down sampled it at 20Hz. Now question is: What will be effect if I vary down sampling from 20Hz to say 5Hz or 60Hz? And why 20Hz is appropriate?

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Given that you have removed all signal content above 10 Hz, your 20 Hz sample rate will be identical to the minimum sample rate based on the Nyquist sampling criterion.

If you instead use 5 Hz, you can only represent a bandwidth of 2.5 Hz and, e.g., a signal appearing to be at 2 Hz might have been a 3, 7 or 8 Hz signal as well (meaning that you can not distinguish between a signal at any of those frequencies after the downsampling). This is caused by aliasing.

Using 60 Hz would be clearly feasible but will consume more storage of the signal. The possible benefit might be that later processing may be simpler as the signal does not cover the whole signal band. However, this depends on which processing is required later. Also, while the processing in itself may be simpler, there are more samples to operate on so the total complexity may not be reduced.

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  • $\begingroup$ Thanks. Couldn't get your second paragraph. What is meant by "a signal appearing to be at 2 Hz might have been a 3, 7 or 8 Hz signal as well (meaning that you can not distinguish between a signal at any of those frequencies after the downsampling). This is caused by aliasing." In last paragraph you said that down sampling at 60Hz will consume more storage. Will not it consume less stotage as now every 60th sample is picked and hence length of the down sampled signal will be very less now.? $\endgroup$ – Muhammad Akmal Feb 25 '14 at 15:57
  • $\begingroup$ Well, the basic meaning is that you will distort the signal through aliasing. The slightly more advanced background is that if you sample a signal at k Hz, the frequency content of that signal can be at most k/2 Hz. The effect of having a signal with a frequency over k/2 Hz, say m Hz (< k Hz for simplicity) is that it will look identical to a signal with a frequency of k-m Hz. Using 60 Hz instead of 20 Hz will consume exactly three times as much storage as you have 60 samples instead of 20 samples per second of data. $\endgroup$ – Oscar Feb 25 '14 at 16:04
  • $\begingroup$ x = [1 2 3 4 5 6 7 8 9 10]; y = downsample(x,3) % y = 1 4 7 10 y = downsample(x,4) % y = 1 5 9 . I am unable to get how will consume more storage when down sampling is increased from 3 to 4. $\endgroup$ – Muhammad Akmal Feb 25 '14 at 16:23
  • $\begingroup$ I meant that the resulting sampling rate is 5 Hz and 60 Hz, i.e., four time less and three times more than 20 Hz. In your setting going from 500 Hz to 5, 20, and 60 would be downsampling factors of 100, 25, and 6.25 respectively. $\endgroup$ – Oscar Feb 25 '14 at 16:30
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By saying you sample your signal,you actually convolve it with a train of impulses spaced apart by Ts (1/f).That results in MULTIPLE COPIES of your signal in the frequency domain. That multiple copies could possibly create problems,resulting of that change in the sampling frequency (you may dont care about that but you may be asked in the future).If the sampling rate is reduced (downsampling) then this copies will EXPAND,(and may overlap with each other) if the sampling rate is increased (up sampling) this will shrink. Now,the limit where you will not have them overlapping is the fundamental frequency range (+-fs/2).That is derived by the Niquist criterion,for sampling and that is why it "should" be kept the frequency range within this limits.

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  • $\begingroup$ I repeat. What will be the effect if I vary down sampling e.g. 5Hz or 60Hz? $\endgroup$ – Muhammad Akmal Feb 25 '14 at 16:03
  • $\begingroup$ I repeat that if you down sample your signal (reducing the sampling frequency) your multiple copies i stated above may OVERLAP,(you need band limiting filters for avoiding the results of overlaping) That in the case you go beyond the limits (determined by Niquist etc).If you increase your signals will shrink.For that effects you will need interpolation filters as well.Have a look at google by searching "multiple copies freq domain down/up-sampling" $\endgroup$ – Giwrgos Rizeakos Feb 25 '14 at 17:37

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