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I am currently analyzing the raw measurements of a sensor with the sampling frequency of 400[hz]. According to Nyquist theorem, the bandwidth must be less than a half of the sampling frequency, which means less than 200 [Hz]. What will happen if I select the bandwidth as 50 [Hz] or 100 [Hz]?

(I have already tried to design two low pass FIR filters with the same characteristics, but different bandwidths, one 200 [Hz] and the other one 50 [Hz]; I noticed that for the bandwidth of 50 [hz], the pass band gain is not 1 anymore).

Thank you

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The FIR filter can only be applied to the signal after it has been digitized, which is too late. You have to apply the anti-aliasing filter before the ADC. That is to say, you need an analog filter.

As far as bandwidth, that depends on your other requirements. If you know that there's only noise above 50Hz, then you could use a 50Hz lowpass as your antialiasing filter, and reduce the noise at the same time.

Using a lower cutoff also makes the analog filter easier to build. A filter that is sharp enough to remove everything above 200Hz but not mess with lower frequencies (much) would need several carefully calculated stages, and might be difficult to build correctly (oddball part values and what have you.) If you use a cutoff of, say, 100 Hz you could get by with a simpler analog filter than if you really, really need frequencies up to 200Hz.

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  • \$\begingroup\$ I see, Therefore it won't modify the pass band gain. Thank you very much \$\endgroup\$ – user3506463 Jun 10 '15 at 9:21
  • \$\begingroup\$ Pardon me? What has anything I said got to do with the passband gain? \$\endgroup\$ – JRE Jun 10 '15 at 9:23
  • \$\begingroup\$ Sorry, I forgot the question mark, it was a question. \$\endgroup\$ – user3506463 Jun 10 '15 at 9:25
  • \$\begingroup\$ The passband gain of your (analog) filter is whatever your design makes it. If you still have an FIR filter in the digital domain, then its passband gain will be whatever you designed (or specified it to be in your design tool.) \$\endgroup\$ – JRE Jun 10 '15 at 9:33
  • \$\begingroup\$ Previously i thought that the bandwidth selection modifies the passband gain itself. The problem which made me confused is, I'm currently working with a sensor and its provided software. I tried to check the measurements and i noticed that when i select the bandwidth of 50, there is an offset in the measurements, (offset is my own description) , and by changing the bandwidth to 200[hz], this offset disappears. at this point i started to design different low pass filters in matlab to see if the bandwidth changes the passband gain of the filter. Now i understood anyway, thank you very much \$\endgroup\$ – user3506463 Jun 10 '15 at 9:50
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According to Nyquist theorem, the bandwidth must be less than a half of the sampling frequency

No, that is the wrong way to look at it.

This is the correct way to look at it: -

The sampling frequency must be at least twice the highest spectral content of the signal you are wishing to digitize or you will get aliasing

Anti-alias filters are in the analogue realm before digitization/ADC

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  • \$\begingroup\$ +1 (or + lots if I could vote more times) This is a very valuable point to me made. \$\endgroup\$ – Michael Karas Jun 10 '15 at 9:19

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