Imagine I have an ideal signal, V, and a noise, W, so that my observed signal is S = V + W. I observe a peak in the range of my measurement, which is associated with a peak in the ideal signal, but not quite the same. So there is an error in the observed peak, as depicted in the figure.
My question is: How to calculate the error of the peak detection based on the analytical features of the ideal signal and the statistical characteristics of the noise? Let's say I have a candidate for the ideal signal which comes from calculation, so for instance I know what the second derivative of V is at the peak. Also, I can extract e.g. the distribution and auto-correlation of W from another region in the observed signal where I expect constant V. Now how can I put these pieces of information together to calculate the error?
I actually expect lots of literature on such basic concepts in signal analysis and noise characterization, but I was not successful in finding any relevant resources. I appreciate any help in this matter by citing literature or providing solution.
Hi Hossein Hassani ,
How about you take FFT of your measurement? If the noise is white and you have a good signal to noise ratio (SNR) then you can always extract the frequencies of your ideal signals and reconstruct an approximation of that using inverse FFT. From the peak of reconstructed ideal signal, you can calculate the peak error. Hope this helps. Best.
The detection would depend on the signal to noise ratio, type of noise, etc.
Refer to Statistical signal processing book(s)
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