# How to get the signal to noise ratio from noisy data set with sinusoid?

I'm new to DSP and trying to do some example problems for a class and am confused by this one.

Given a data set, and knowing it contains a signal that is a single sinusoid with random content noise, how can I calculate the signal to noise ratio? I also have the sampling rate.

I have been able to plot the autocorrelation, and can see the characteristic peak at 0 to indicate the noise. I'm just unsure if I can get the power of the signal and noise from this autocorrelation, or the power spectra density (taking the fft of the autocorrelation). Do I need to find the amplitude, frequency, and phase of the sinusoidal signal and subtract it from the original to do this? If so, how do I find those?

Any help is appreciated, I am new to DSP and learning to thanks!

## 1 Answer

One method is to pass the noisy sinewave through a notch filter tuned to the sine wave frequency. The output of the notch filter is N and the input is S + N. S/N = (S + N)/N - 1. This is the way some analog meters work.

• this will also include distortion, though – endolith Jun 20 '14 at 20:02
• Yes, this method computes SINAD = signal to noise and distortion. – John Jun 21 '14 at 2:21