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Assume I have a signal that oscillates between 10KHz and 9Khz every 500msec (Change happens linearly, so at t=0, it is 10KHz and it goes to 9.5Kz at t=250msec and 9KHz at t=500msec and frequency start to increase and goes back to 10KHz at 1 sec and this goes on)

Assume I sample this signal at 50Khz and I do fft to find out what's the frequency. But due to sampling rate, I have to accumulate some samples where the interest frequency is slowly shifting.

If I were to sample at 500KHz or even 5MHz, can I get a better SNR? (The assumption here is that I can sample for a shorter duration -still several cycles of the target frequency in time domain- and this will provide a less spread signal in a given time and better fft snr. )

My gut tells me, this won't help but I like to ask the crowd.

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    $\begingroup$ You are just looking in the sample rate for SNR. i think that the bith dept of your AD-converter is more important. With a very high sample rate you just measuring just the same value... $\endgroup$
    – Jan-Bert
    Apr 14, 2016 at 10:31
  • $\begingroup$ I realize this is an old question, but I think both the answers and comments omit an important point. If your signal has a single frequency, sampling more densely will improve the SNR of your amplitude estimate, but if it reduces your sampling duration (e.g., your number of samples is constant), that amplitude SNR comes at the expense of frequency resolution (and frequency SNR). The same tradeoff applies when you estimate instantaneous frequency of a variable frequency (e.g., chirped) signal. $\endgroup$
    – rjonnal
    May 17, 2022 at 4:37

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Your instincts are right. You won't increase SNR by increasing sampling rate because you also have more noise samples. The overall signal energy and noise energy does not depend on sampling rate.

But, I believe you are mixing up two problems. In your case the frequency is not constant, therefore Fourier based analysis yield less than optimal results. Your problem is in the signal itself, not the signal to noise ratio. You can have a look at the high-order ambiguity function (try this or that) or the Wigner-Ville transform. Those are more suitable for linearly changing frequency.

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  • $\begingroup$ It's true that you have more noise samples, but if you want to estimate instantaneous frequency, you have to do a little integration over time, and dense sampling improves amplitude SNR. For normally distributed noise it will improve amplitude SNR by sqrt(N), given N samples. Sparse sampling over longer durations improves frequency precision (or SNR). $\endgroup$
    – rjonnal
    May 17, 2022 at 4:45
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You haven't told us what is the goal of your processing. If you're trying to estimate the instantaneous frequency of your signal then I agree with ThP, the FFT is not the best approach. To measure the instantaneous frequency of your signal I suggest you perform FM demodulation. The FM demodulation schemes I'm familiar with have better performance the higher the data sample rate. So, I suggest you sample your signal at a rate that's several times higher than the minimum rate required by the Nyquist criterion and perform FM demodulation. If you need guidance on how to perform FM demodulation, let us know.

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  • $\begingroup$ My goal is to detect a low SNR signal. I can sample at a higher frequency but I don't fully understand how FM demodulation will help. Because the incoming signal is not FM modulated. $\endgroup$
    – Ktuncer
    Apr 21, 2016 at 4:29
  • $\begingroup$ @Ktuncer, As I wrote before, I’m not sure what is the goal of your processing. If you are not trying to detect the instantaneous frequency of some signal then what I wrote previously will be of no value to you. Good Luck. $\endgroup$ Apr 23, 2016 at 14:06

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