Wavelet Covariance Transform code in Matlab

Can someone please give a link to code/flowchart for executing Wavelet covariance transform of a function in matlab? Thanks

[Wayne King]

Santino, Can you please explain in more detail what you mean by the "wavelet covariance transform" of a function. Are you sure you don't mean wavelet coherence between two functions?

Or do you mean, given some data, how do I compute the wavelet autocorrelation (autocovariance) for that data?

[Santino M]

Hi Wayne. The problem statement goes like this. Given a time series data, the inflection points (or points of maximum change w.r.t time) need to be found. A Haar function is used along with integration to get wavelet covariance transform. Details are given in Section 2 of the link pdf. I need to know how it can be executed in matlab.Thanks. http://journals.ametsoc.org/doi/pdf/10.1175/1520-0426(2003)020%3C1092%3AFBLTAO%3E2.0.CO%3B2

Answer 1

[Christiaan]

Dear Santino,

What you could do is to create two functions, where in the first one, the function f(z) times h is calculated and in the second file the integral is computed.

This would be the mfile to compute the function_fz_times_h:

function fz_times_h = function_fz_times_h(z,a,b) 

fz = exp(z).*log(z);  % <-- here write your own function inside
if (z<=b)|(z>=(b-a/2))
    h=1;
elseif (z>=b)|(z>=(b+a/2))
    h=-1;
else
    h=0;
end

fz_times_h = fz*h;

Then in this mfile you define the covariance transform of the Haar function:

function w_f = function_wf(a,b,z_b,z_t) 

w_f = 1/a*quadgk(@(z)function_fz_times_h(z,a,b),z_b,z_t);

And then in the main file you can compute directly the covariance transform of the Haar function:

clc;clear all;close all; 

a = 1;      b = 1; 
z_b = 0;    z_t = 1;

wf=function_wf(a,1,0,1)

Good luck! Christiaan