how to receive power values in and out the cone of influence in wavelet transform.

Hi you!

I wish you could help me. I have a data set and need to find periods in it by wavelet transform. How to receive power values in and out the cone of influence in wavelet transform.

Answer 1

[Mathieu NOE]

hello

I assume this is related to your previous post

How to plot power of wavelet transform. - MATLAB Answers - MATLAB Central (mathworks.com)

I will answer on this one to make follow up simpler

[Dung Nguyen]

Hello

Thanks for your answer.

Yes, my this question is related to my previous question. I plotted the curve of the power but the result is not expected. So I want to obtain the power values which in and out the cone of influence. Then I try to plot only power values in the cone of influence.

Other problem which I am having trouble, I was hope that my data show period aproximately 2 years but when I use wavelet transform I didn't receive that. So I think that I can remove power values out the cone of influence and only recerive power values in the cone of influence if it can show period 2 years.

Looking forward to your reply

[Mathieu NOE]

hello

I am not sure what the purpose of splitting the data between in / out of the cone of influence can bring - simplest thing to do would be simply to hide the out of COI data by putting alpha factor to one

regarding the second issue , I also tested the data with regular spectrogram technique, but also here there is no evidence of a 2 years period (I believe I remember this issue was already discussed in the past) . What can make you so sure that the data shall have a 2 years period ? this is obviously not show by neither the CWT nor the spectrogram plot.

plot with alpha = 1 :

code :

% close all;clc;clear all;
% function [varargout]=wt(d,varargin)
% function [varargout,power,period]=wt(d,varargin)
function main
close all;clear all;clc;
%% Continous Wavelet Transform
% Creates a figure of wavelet power in units of
% normalized variance.
%
% USAGE: [wave,period,scale,coi,sig95]=wt(d[,params])
%
% d: a time series
% wave: the wavelet transform of d
% period: a vector of "Fourier" periods associated with wave
% scale: a vector of wavelet scales associated with wave
% coi: the cone of influence
%
% Settings: Pad: pad the time series with zeros?
% .         Dj: Octaves per scale (default: '1/12')
% .         S0: Minimum scale
% .         J1: Total number of scales
% .         Mother: Mother wavelet (default 'morlet')
% .         MaxScale: An easier way of specifying J1
% .         MakeFigure: Make a figure or simply return the output.
% .         BlackandWhite: Create black and white figures
% .         AR1: the ar1 coefficient of the series
% .              (default='auto' using a naive ar1 estimator. See ar1nv.m)
%
% Settings can also be specified using abbreviations. e.g. ms=MaxScale.
% For detailed help on some parameters type help wavelet.
%
%
% Example:
%      wt([0:200;sin(0:200)],'dj',1/20,'bw','maxscale',32)
%
% (C) Aslak Grinsted 2002-2014
%
% http://www.glaciology.net/wavelet-coherence

% -------------------------------------------------------------------------
%The MIT License (MIT)
%
%Copyright (c) 2014 Aslak Grinsted
%
%Permission is hereby granted, free of charge, to any person obtaining a copy
%of this software and associated documentation files (the "Software"), to deal
%in the Software without restriction, including without limitation the rights
%to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
%copies of the Software, and to permit persons to whom the Software is
%furnished to do so, subject to the following conditions:
%
%The above copyright notice and this permission notice shall be included in
%all copies or substantial portions of the Software.
%
%THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
%IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
%FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
%AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
%LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
%OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN
%THE SOFTWARE.
%---------------------------------------------------------------------------


% ------validate and reformat timeseries.
% load Lat.txt
% [dt,d]=textread('Lat.txt','%f%f','delimiter','whitespace');
Lat=load('TEC.txt');
% [dt,d]=formatts(Lat);
% 
% n=size(d,1);
% sigma2=var(dt(:,2));

[d,dt]=formatts(Lat);
n=size(d,1);
sigma2=var(d(:,2));

%----------default arguments for the wavelet transform-----------
Args=struct('Pad',1,...      % pad the time series with zeroes (recommended)
    'Dj',1/12, ...    % this will do 12 sub-octaves per octave
    'S0',2*dt,...    % this says start at a scale of 2 years
    'J1',[],...
    'Mother','Morlet', ...
    'MaxScale',[],...   %a more simple way to specify J1
    'MakeFigure',(nargout==0),...
    'AR1','auto');
varargin = [];
Args=parseArgs(varargin,Args,{'BlackandWhite'});
% Args=parseArgs(Lat,Args,{'BlackandWhite'});
if isempty(Args.J1)
    if isempty(Args.MaxScale)
        Args.MaxScale=(n*.17)*2*dt; %automaxscale
    end
    Args.J1=round(log2(Args.MaxScale/Args.S0)/Args.Dj);
end

if strcmpi(Args.AR1,'auto')
    Args.AR1=ar1nv(d(:,2));

    if any(isnan(Args.AR1))
        error('Automatic AR1 estimation failed. Specify it manually (use arcov or arburg).')
    end
end



%----------------::::::::---------- Analyze: ---------:::::::::::::-----------------


[wave,period,scale,coi] = wavelet(d(:,2),dt,Args.Pad,Args.Dj,Args.S0,Args.J1,Args.Mother);

t=d(:,1);
power = (abs(wave)).^2 ;        % compute wavelet power spectrum
signif = wave_signif(1.0,dt,scale,0,Args.AR1,-1,-1,Args.Mother);
sig95 = (signif')*(ones(1,n));  % expand signif --> (J+1)x(N) array
sig95 = power ./ (sigma2*sig95);
Yticks = 2.^(fix(log2(min(period))):fix(10));
subplot('position',[0.1 0.37 0.65 0.48]);
% subplot('position',[0.77 0.37 0.2 0.48]);
if Args.MakeFigure
    H=imagesc(t,log2(period),log2(abs(power/sigma2)));%#ok,log2(levels));  %*** or use 'contourfill'
    %logpow=log2(abs(power/sigma2));
    %[c,H]=contourf(t,log2(period),logpow,[min(logpow(:)):.25:max(logpow(:))]);
    %set(H,'linestyle','none')

    clim=get(gca,'clim'); %center color limits around log2(1)=0
    clim=[-1 1]*max(clim(2),3);
    set(gca,'clim',clim)

%     HCB=colorbar;
%     set(HCB,'ytick',-7:7);
%     barylbls=rats(2.^(get(HCB,'ytick')'));
%     barylbls([1 end],:)=' ';
%     barylbls(:,all(barylbls==' ',1))=[];
%     set(HCB,'yticklabel',barylbls);


    set(gca,'YLim',log2([min(period),max(period)]), ...
        'YDir','reverse', ...
        'YTick',log2(Yticks(:)), ...
        'YTickLabel',num2str(Yticks'), ...
        'layer','top')
    %xlabel('Time')
    ylabel('Period')
    hold on



    [c,h] = contour(t,log2(period),sig95,[1 1],'k'); %#ok
    set(h,'linewidth',2)
    %plot(t,log2(coi),'k','linewidth',3)
    tt=[t([1 1])-dt*.5;t;t([end end])+dt*.5];
    hcoi=fill(tt,log2([period([end 1]) coi period([1 end])]),'w');
    set(hcoi,'alphadatamapping','direct','facealpha',1)
    hold on
%     
% p1 = [log2(26),0];
% p2 = [log2(26),4749];
% 
% p3 = [log2(183),0];
% p4 = [log2(183),4749];
% 
% p5 = [log2(340),0];
% p6 = [log2(340),4749];
% 
% p9 = [log2(1000),0];
% p10 = [log2(1000),4749];
% 
% plot([p1(2),p2(2)],[p1(1),p2(1)],'--','Color','k','LineWidth',1.0)
% hold on
% plot([p3(2),p4(2)],[p3(1),p4(1)],'--','Color','k','LineWidth',1.0)
% hold on;
% plot([p5(2),p6(2)],[p5(1),p6(1)],'--','Color','k','LineWidth',1.0)
% hold on;
% %plot([p7(2),p8(2)],[p7(1),p8(1)],'--','Color','r','LineWidth',1.5)
% % hold on;
% plot([p9(2),p10(2)],[p9(1),p10(1)],'--','Color','k','LineWidth',1.0)
% %     hold off
% % subplot('position',[0.77 0.37 0.2 0.48])
end
subplot('position',[0.77 0.37 0.2 0.48])
% s=sum(power,2)./10000000;
s=sqrt(sum(abs(power).^2,2));
plot((s),log(period));
% plot(s,log2(period));
Yticks = 2.^(fix(log2(min(period))):fix(log2(max(period))));
% levels = [0.0,0.1,0.2,0.3,1,2,4,8,16] ;
levels = [0.0625,0.125,0.25,0.5,1,2,4,8,12] ;
hold off
    set(gca,'box','on','layer','top');
% varargout={wave,period,scale,coi,sig95};
% varargout=varargout(1:nargout);
figure(2);
plot(s,log2(period));

[Dung Nguyen]

Hello

Thanks for your help.

Here, I didn't say clearly. There is a s=sqrt(sum(abs(power).^2,2)) variable in code. I want to calculate s values only in the cone of influence. Then I can plot the curve of s vs period (subplot is the right) which values is only in the cone of influence. I think when I calculate s as above, I received total of s values in and out the cone of influence and I want to seperate them. But I don't know how to do that.

According to you said: "I also tested the data with regular spectrogram technique, but also here there is no evidence of a 2 years period (I believe I remember this issue was already discussed in the past)" ....>Yes. I am doing my studies and Unfortunately, the results are not good as I expected. So I want to receive s values only in the cone of influence and considering if I can find any things which the same period 2 year (may be >2years, ex: 28-34 months).

Looking forward to your reply

[Mathieu NOE]

hi again

sorry if I'm not understanding the point but eliminating the data out of the COI either mathematically (i.e. replaced by zeros or nans) or simply visually by shading this area (as it is done today) will not change anything to the data in the COI.

I still don't get why you think this is key to finally see a supposed correct output showing the 2 years period

are you sure that someone else could tell from these data that he/she could find that 2 years period ??

all the best

[Dung Nguyen]

Thanks for your help.

I'm sorry because my english is not good. According to what you said I understand that s=sqrt(sum(abs(power).^2,2)) which I will receive to not change the power curve if I remove them which out the cone of influence. Is my thinking correct?

Here I attached package and results. Do you have any way to calculate the s values inside COI and outside COI?

I still don't get why you think this is key to finally see a supposed correct output showing the 2 years period

are you sure that someone else could tell from these data that he/she could find that 2 years period ??....>Not yet. We expected such results to appear when processing the data. But it seems it failed