1
$\begingroup$

I have multiple data sets of the same signal measured using the same hardware and I want to know what sort of techniques I can use to improve the SNR.

I was thinking if I adjust and ensure they have the same phase, i could coherently add them, but I didn't really see an improvement in SNR. I'm guessing the reason for this is because the noise gets added together as well.

It makes me wonder two things:

  • What are some valid ways to combine like signals, to improve SNR

  • Is there any way to exploit the similarity in signals to reduce noise?

Thank you

$\endgroup$
  • 1
    $\begingroup$ Coherent addition should reduce noise, provided the noise is iid across the datasets and is independent of the signal. eg. with additive Gaussian distributed noise, coherent addition of N observations should reduce noise variance by a factor of N. There are surely many ways to exploit similarity in signals, but you'll have to provide more details about your system and measurement model. $\endgroup$ – Atul Ingle Oct 5 '17 at 15:03
  • $\begingroup$ I rather say what matters is noise model. $\endgroup$ – AlexTP Oct 5 '17 at 16:36
2
$\begingroup$

Coherent Gain happens when you have copies of the same signal but different noise. If the noise is independent in each copy, the gain should be $10log N$ dB where $N$ is the number of copies. For a well crafted measurement system, additive electronic noise should be independent. Things like ambient noise will have some correlation provided a reasonable distance between sensors and $5logN$ is a reasonable lower expected gain.

If you don’t see at least $5 log N$ dB, then there is probably something wrong. Coherent Gain works. If it didn’t, many here would not have jobs.

You might try cross correlating pairs of your copies as a diagnostic. Without knowing your data, I cant say with certainty that you should see a well defined peak but the absence of a well defined peak would be a cause for concern

| improve this answer | |
$\endgroup$
2
$\begingroup$

Each of $C$ different collections, with signal mean $\mu$ and zero-mean iid noise of variance $\tau$ has SNR (in power) $\frac {\mu^2} {\tau}$

By linearity of expectation, the summation of these collections will have a signal level $C\mu$ and variance $C\tau$, with SNR $\frac {(C\mu)^2} {C\tau}$, yielding a power gain of $C$.

Converting power to dB, the gain of C similar signals is $10 log_{10}(C) \approx 3$ dB per doubling the number of collectors.

If your signals are not same-level with iid noise, then you might want to check out Maximal Ratio Combining, or Wiener Filters.

| improve this answer | |
$\endgroup$

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.