Hi Rhenan!

To obtain confidence interval (CI) i use another approach. For probability level alpha=0.9972 (look for 3sigma rule) I solve two equation for left and right boundary.

(1-alpha)/2=integral(PSD(x),-inf,x);

(1+alpha)/2=integral(PSD(x),-inf,x);

if you solve it, you will find left and right boundaries of CI.

Hi Oleksii Vodka, thank you very much! I'll implement a code to solve these equations.

But to use the 3sigma rule the PSD distribution must be normal?

No. I mean that alpha=0.9972 is probability under normal low with 3sigma rule. But you can define alpha in another way.

Rhenan, have you looked at the following article?

Torrence, C. & Compo, G. P. A practical guide to wavelet analysis Bulletin of the American Meteorological Society, American Meteorological Society, 1998, 79, 61-78

It's mostly about wavelet analysis and significance tests. Section 4 explains theoretical spectrum and significance levels for both wavelets and Fourier spectra. I have translated their code from Matlab to Python, included some improvements and also received contributions from other people around the globe who found a couple of mistakes. My code is available at https://github.com/regeirk/pycwt

The lines of code that calculate the significance of a given signal are in module wav.py (579--712).

Enjoy!

Hi Sebastian Krieger, thank you very much!

I just figured out last sunday how to find the inverse cdf of the chi squared using chi2.ppf([1 - alpha / 2, alpha / 2], 2 * dof), just like you did in your code.

By the way, great job with your wavelet module!

Hi Sebastian Krieger

I was trying to implement the reconstruction formula of a test signal using the relation of TC98 with your code in python but i don't get the same result of the original. Do you ever try to do that?