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While researching SNR improvement techniques, I came across many techniques, mostly the application of digital filters and windowing. Shortly, I read an article that said that performing decimation can be used to improve the SNR of a signal, by a factor of 3dB (half in linear terms) for every time the decimation is doubled.

From my understanding of decimation, we basically throw away a certain portion of samples for every few samples taken, meaning that if we have a decimation of 3, we only keep 1 of every 3 sampled, discarding the other two. Would it be possible for anyone to explain to me, whether or not this is true? Can decimation be used as a SNR improvement technique? And if yes, why?

Edit: I forgot to mention that I also read that decimation first applies a low pass filter, before discarding the samples. Is this true? And if yes, how would this be implemented? Would this be the construction of a (digital) FIR filter?

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  • \$\begingroup\$ Yes. If my bare bones understanding is correct, sigma delta filters do this by noise shaping which moves the noise to higher frequencies and then decimating it. \$\endgroup\$ – DKNguyen Nov 14 at 21:17
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Decimation basically means downsampling or re-sampling the signal using a lower sample rate, see the article on Wikipedia.

There are several ways to do the decimation and it depends on the chosen method and the type of signal what effect decimation has.

When as in your example, the 1 out of 3 samples is kept and that is combined with lowpass filtering (the filtering might be needed to avoid aliasing) then I can understand how that could increase the SNR. If the noise content is mainly in higher frequencies (higher than the signal's frequencies) then the noise will be filtered out while the signal should remain mostly unaffected.

A different well known method for downsampling is to take the average value of multiple samples. Then additional filtering might not be needed. Note that the averaging does introduce a low-pass filtering effect but in the digital domain. Again if the noise is mainly at high frequencies part of that will be filtered out which improves the SNR.

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Taking samples of a digital stream of data is subject to the same impositions as when sampling an analogue signal. To effectively sample an analogue signal, you need an anti-alias filter to remove unwanted higher frequency artifacts that can bounce down into the digital domain's restricted bandwidth and cause aliasing.

The same applies when converting to a lower sampling rate (or down-sampling or decimation); to do this properly you must remove higher frequency artifacts in the higher rate data or you will get aliasing. This is done by filtering (FIR, IIR or simple averaging).

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