3
$\begingroup$

I did not manage to find clear answers to this question: does decimation after an appropriate lowpass filter improve the signal to noise ratio?

To investigate this question, I considered data generated by a sine plus some random noise. The FFT shows a very clear peak (two with the symmetry). If I naively downsample without filtering, the signal gets aliased and the SNR decreases, which makes sense: I removed relevant information about the sine while keeping the noise unchanged. Then, I applied a lowpass filter to avoid aliasing when subsampling. The SNR did not seem to significantly change.

This question is of practical importance: when measuring a phenomenon, say at 1Hz, is it useful to use a very high sampling frequency such as 1kHz or more in order to improve the SNR by filtering and decimating (given that the memory and computational cost is not a problem, of course)?

$\endgroup$
4
$\begingroup$

So, let's not forget what SNR is: it's a relation of powers present.

The thing that improves SNR is a propoer low-pass: it leaves the signal power alone and reduces the power of the noise.

An ideal low-pass filter will leave zero noise outside its specified bandwidth – so it doesn't matter whether you "cut off" these bandwidths using decimation or not, from a pure SNR perspective.

This question is of practical importance: when measuring a phenomenon, say at 1Hz, is it useful to use a very high sampling frequency such as 1kHz or more in order to improve the SNR by filtering and decimating (given that the memory and computational cost is not a problem, of course)?

Yes! That is called oversampling, and it's useful for a couple of reasons, foremost for doing so-called noise shaping, which allows you to get a lower noise floor in your band of interest. With appropriate filtering, you do get a lot of SNR gain.

This is actually done pretty often; Software Defined Radio devices often run at dozens to hundreds of Megasamples, no matter how much bandwidth you want to observe, and do the filtering and decimation in-device. That way, you get the oversampling benefits, and also, you don't waste money and potential phase linearity etc by implementing steep-edged analog anti-aliasing filters, but can get away with much more relaxed filter specs.

$\endgroup$
  • $\begingroup$ And what about the SNR restricted to the bandwidth of the low pass filter? If I understand correctly, it is unchanged. $\endgroup$ – anderstood Aug 22 '16 at 14:28
  • $\begingroup$ well, yeah. That's the idea of restriction. But: it kind of contradicts the idea of specifying an SNR if you just pick the part of noise that is within a specific bandwidth; the whole bandwidth of your noise distorts your observation. $\endgroup$ – Marcus Müller Aug 22 '16 at 14:42

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.