I have a digitized acoustic data of length L in which a pulsed signal (chirp) of finite duration and bandwidth is merged starting at some time instant t1 and ending at time instant t2. I wan to calculate SNR of this pulse signal. What is the best way to calculate this SNR?
Thanks & Regards
Use the time before or after the chirp to compute the noise level. As long as you know t1 and t2, you can get the amplitude of signal + noise. So your SNR is just ((signal + noise) - noise) / noise. If you can actually extract the signal it will be a lot more accurate, especially if the signal is really small compared to the noise. If there are a lot of pulses that are all the same, averaging over 100's of samples will improve the results.
Dr Mike mentioned a way that may work in the time domain, especially if you have enough "quiet" time before and after the signal to get sufficient noise statistics.
Depending on the oversample rate, a similar thing may be able to be done in the frequency domain, where the noise level outside of the signal is determined, and then the S+N level within the signal BW is determined. (S+N)/N can then be adjusted to find SNR.
Ideally the region of the signal has reasonably flat spectrum and the region of the noise has reasonably constant spectral density. If not, you may need to be careful in interpreting the results. This is also true with the time domain method if the signal or noise statistics aren't stationary during the processing period.
You could even do both methods and if you reach comparable answers then you can reasonable confidence in the result.
I have read the responses from Dr. Mike and Slartibartfast, and their ideas are completely valid, and should work.
Here are some other ideas.
How much do you know about the chirp? Can you derive its parameters?
If you can reproduce the chirp in some decent sense, then you can cancel it from the combined signal, either manually, or with adaptive filtering. I have done this type of thing sometimes, by manually choosing the parameters, and iterating the subtraction of the estimated chirp from the combined signal and noise, and measuring the residual power (the noise level). Once you reach the minimum residual to your level of satisfaction, you have the signal power too, because you have reconstructed a good estimate of the chirp.
I think there are only a few chirp parameters to estimate here.
- The amplitude of the chirp
- The starting phase
- The starting frequency
- The ending frequency
- The start time
- The end time
- The rate of the frequency trajectory (derived from 3-6 above)
If the chirp is moving slowly across the frequency band, then something like an adaptive line enhancer might allow you to acquire some of its characteristics, or even roughly calculate the SNR, as one of the outputs from the ALE is the residual noise, and the other is the predicted signal.
If you can do DFTs of e.g. t2-t1/2 then in the DFTs the chirp signal will be contained only in part of spectrum. The chirp portion in DFT will be flat (signal power) and the other frequencies will be almost noise, so you can measure noise from lowest power spectrum.
Not sure about this but can be an idea ;)