What this code line means in Inverse Wavelet Transformation(icwtft)?

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Hi, All
I am trying to modify the function of wavelet transformation, and I found this code in icwtft function,
% Real part of the wavelet transform.
Wr = real(cwtcfs);
% Compute the sum.
scales = S.scales(:);
repSca = repmat(scales,[1,size(cwtcfs,2)]);
summand = sum(Wr./sqrt(repSca),1);
% Compute the constant factor.
wft = waveft(S.wav,S.omega,scales);
Wdelta = sum(wft,2)/N;
RealWdelta = real(Wdelta);
RealWdelta = RealWdelta(:);
C = sum(RealWdelta./sqrt(scales));
% Compute the inverse transform.
mulWAV = get_mulWAV(S.wav);
Xrec = (1/C)*summand;
Xrec = (Xrec-mean(Xrec))/mulWAV + S.meanSIG;
nbSamp = length(Xrec);
and I read the reference journal, but I could not understand why we need to obtain 'mulWAV' for inverse wavelet transformation.
Any ideas and comments would be very helpful. Thanks in advance!
  3 Comments
Yutaro Umekawa
Yutaro Umekawa on 28 Jul 2015
Thank you for your comments. Sorry for inconvenient question.
I mean, there is the extension code "Xrec = (Xrec-mean(Xrec))/mulWAV + S.meanSIG;" which I can not find in the original journal; (Torrence, C. and G.P. Compo "A Practical Guide to Wavelet Analysis", Bull. Am. Meteorol. Soc., 79, 61–78, 1998.) in matlab function icwtft.
I read this journal and understand the numerical expression of inverse wavelet transformation, but I could not find any sentences that the reconstructed signal can be divided by mulWAV value (I still do not understand what does mulWAV mathmatically means in the equation for the reconstruction)
So, I would like to know why this extension code is needed. Thanks for your help.

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