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I'm trying to calculate the SNR of a sine wave produced with a 12 bit DAC. I'm new when it comes to calculating/measuring noise in signals. My idea was to capture the signal using an oscilloscope (which unfortunately does not have an FFT function), so I could run an FFT analysis in MATLAB to separate the signal in its fundamental and harmonics to find the SNR.

This is the signal that I acquired, it's a 600 mVpp sine wave at 1kHz

1kHz sine wave

I have 625000 samples, and according to the metadata from the oscilloscope, it has a sample interval of 1.6e-8s. My first approach was to use MATLAB's snr function directly using the voltage samples

Fs = 625000;
r = snr(measurements, Fs);

Using that code I obtain this: snr result

I was expecting the fundamental to be close to 1kHz, but it's sitting at 0.011 kHz with -9.699 dB. Is this result expected?

I also tried plotting the FFT using the following code (which again gives me this peak close to 0):

y = fft(measurements);
n = length(measurements);                         
fshift = (-n/2:n/2-1)*(625000/n);
yshift = fftshift(y);
plot(fshift,abs(yshift))

fftshift

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    $\begingroup$ [value, index] = max(abs(y)) and freqFundamental = fshift(index) $\endgroup$ – Ben Jul 21 at 11:36
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    $\begingroup$ Your Fs is off by a factor of a hundred $\endgroup$ – Dan Szabo Jul 21 at 13:28
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    $\begingroup$ You're right Dan, thanks for pointing that out $\endgroup$ – DCrown Jul 21 at 19:04
  • $\begingroup$ The artifact at 0.11kHz is most likely because you're hard-windowing the signal (by truncating it in the O-scope) before you take the FFT. There's not much you can do about this. $\endgroup$ – TimWescott Jul 22 at 15:07
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For all the reasons above, an oscilloscope is inadequate to this task. Here's a couple of alternatives:

Method 1: find someone with a really good spectrum analyzer, and borrow time on it.

Method 2: build a really good notch filter (for a one-off you'll want to use analog components, and good ones). Characterize it (I didn't say this would be easy). Then run your 1kHz signal through the notch and look at the remainder in the O-scope. Once you get rid of the 1kHz tone, whatever remains is the stuff you don't want -- characterize that, add the 1kHz tone back in on paper, and you've characterized the net effect of your DAC and your notch filter.

Note that method 2 requires some significant analog chops. If your go-to solution involves white proto-board, junkbox capacitors and LM741 amps, you probably need to up your game.

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First, how is your sine wave generated? Based on the first plot, the period seems to be about ~ 1 kHz,

Second, how did you identify where the peak is? You should use a Matlab command like

[value, index] = max(abs(y)) and freqFundamental = fshift(index) 

instead of zooming in on the plot.

Third, you have a 12-bit DAC and you sample the output with an oscilloscope. Oscilloscopes have really fast ADCs but they are not high-precision, they are usually 10-bit ADCs. With oversampling you can still get a resolution higher than 10 bits but I wouldn't use an oscilloscope to precisely characterize the SNR of a given device.

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    $\begingroup$ 1. The sine wave is generated using a programmable DAC which has a frequency word of 26 bits, effectively giving a resolution of 0.25Hz. In terms of the amplitude it has a resolution of 390.63 microV. 2. I'm still not sure on how to do that, I ran the code providded I got the array index in which one of the peak is located. 3. I know that there are specilised instruments for this (quite expensive I assume), I was just wanted to have a quick estimaition of the noise in the singal. $\endgroup$ – DCrown Jul 21 at 16:56

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