I am working on noise processes in electronic devices for my studies, by now Ive been doing a fairly large amount of processing of time measurements, like calculate PSD, estimate thermal, flicker noise, noise filtering, etc. s I would like to get into the more theoretical aspect of noise, and noise analysis in the time domain, because sporadically I see a strange behaviour in the signal and was thinking that maybe some statistical methods could help improve the estimation of the magnitude Im trying to obtain.

I have a reasonable background in probability and statistics, I feel confident with RV, distributions, derived distributions, moments.

Looking for books that could help me start from there (not too basic or advanced), I found RM Gray book "Introduction to Statistical Signal Processing". There doesnt seem to be many other options, I also saw Hayes book but its more for digital systems. By now Im focusing on analog signals.

Ive been trying to read this book a lot, and I hate to say this, because Im really grateful for people writing books to help others but at least for me it has been really bad. It puts a lot of attention on mathematical oddities. From a formal point view probably it is very elegant, but it feels frustrating to have to read a 100 pages for the definitions of a probability space, random variables and random processes.

Do you have any other recommendation? Thanks!

  • $\begingroup$ Your focus seems to be on the modeling of noise generation mechanisms in electronic devices ? That's more of a physical problem than the pure mathematical concern of statistical signal processing. Anyway you can also have a look at H.Stark's book... $\endgroup$
    – Fat32
    Commented Aug 24, 2021 at 2:12
  • $\begingroup$ Thank you for your answer! No, my focus is not on the physical part. To put an example, If I have a temperature sensor, I know the temperature in the atmosphere changes slowly, so high-amplitude spikes in the signal are unlikely and probably caused by noise. The question is how to best filter the signal to obtain the best SNR. I can see from the noise PSD that its mostly flicker, but I am not completely sure the noise process is ergodic, for example if the noise power depends on humidity which could be unrelated to temperature. $\endgroup$
    – Ralph
    Commented Aug 24, 2021 at 2:34
  • 1
    $\begingroup$ I would recommend Statistical Signal Processing by Steven Kay. There are two volumes. The first volume is about detection theory and the second is about estimation theory. Most of the examples covered in the book are based on models with Gaussian noise, but they will help you learn the basics. $\endgroup$
    – Maxtron
    Commented Aug 24, 2021 at 5:14
  • $\begingroup$ Thanks, Ill take a look at Kays book :) $\endgroup$
    – Ralph
    Commented Aug 24, 2021 at 16:18

1 Answer 1


Something like Bendat and Piersol's Random Data Analysis might be a good starting point. It's written more for physical scientists rather than people doing estimation and detection theory like the references in the comments (Gray, Kay, etc.). For specifically spectral analysis, Percival and Walden's Spectral analysis for physical applications was recently updated (i think in 2019 or 2020) under a slightly different name, which you can check out as well.

Different fields also have various data analysis books for them, and there are various handbooks available on different types of sensors, e.g. Fraden's Handbook of Modern Sensors has some overviews of a bunch of physical sensors.


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