function X = imodwt(WJt, VJt, att)% imodwt -- Calculate the inverse (partial) maximal overlap discrete wavelet transform (IMODWT).%%****f* wmtsa.dwt.modwt/imodwt%% NAME%   imodwt -- Calculate the inverse (partial) maximal overlap discrete wavelet transform (IMODWT).%% USAGE%   X = imodwt(WJt, VJt, att)%% INPUTS%   * WJt        -- MODWT wavelet coefficents (N x J x NChan array).%   * VJt        -- MODWT scaling coefficients (N x {1,J} x NChan vector).%   * att        -- MODWT transform attributes (struct).%% OUTPUT%   * X          -- reconstituted set of observations (vector).%% DESCRIPTION%   imodwt computes the reconstituted time series from the MODWT wavelet%   and scaling coefficients.%  %% EXAMPLE%   X = imodwt(WJt, VJt, att);%% ERRORS  %   WMTSA:InvalidNumArguments       =  'Invalid number of arguments specified in function call'%   WMTSA:InvalidWavelet            =  'Invalid wavelet filter specified'%% NOTES%   1. Tests indicate othat riginal and reconstituted time series agree within a %      precision of 10^-11, which is larger than the 10^15 numeric precision.%  %   2. If the MODWT was calculated using 'reflection' boundary%      conditions, which extends the time series, and the  computed coefficients, %      have been truncated to the length of the original series.  The inverse MODWT %      will yield a reconstituted time series that differs from the original.  %      If using 'reflection' boundary conditions, compute the MODWT with the %      opt.TruncateCoefs = 0 option (the default) to compute IMODWT which%      yields and exact replica of the original.% % ALGORITHM%   See pages 177-179 of WMTSA for description of Pyramid Algorithm for%   the inverse MODWT.%% REFERENCES%   Percival, D. B. and A. T. Walden (2000) Wavelet Methods for%   Time Series Analysis. Cambridge: Cambridge University Press.%% SEE ALSO%   modwt, imodwtj%% TOOLBOX%   wmtsa/dwt%% CATEGORY%   modwt%% AUTHOR%   Charlie Cornish%% CREATION DATE%   2003-05-01%% COPYRIGHT%   (c) 2003, 2004, 2005 Charles R. Cornish%% REVISION%   $Revision: 632 $%%***% $Id: imodwt.m 632 2006-08-02 06:15:14Z ccornish $usage_str = ['Usage:  [X] = ', mfilename, ...             ' (WJt, VJt, att)'];  %% Check input arguments and set defaults.error(nargerr(mfilename, nargin, [3:3], nargout, [0:1], 1, usage_str, 'struct'));%% Get the wt filter coefficients.if (isstruct(att.WTF))  wtf_s = att.WTF;  ht = att.h;  gt = att.g;elseif (ischar(att.WTF))  wtf_s = modwt_filter(att.WTF);  ht = wtf_s.h;  gt = wtf_s.g;endN             = att.NX;NW            = att.NW;J0            = att.J0;NChan         = att.NChan;boundary      = att.Boundary;%% Pre-allocate memory.Vout = NaN([N,NChan]);X    = NaN([N,NChan]); %% Do the IMODWT.for (i = 1:NChan)  if (att.RetainVJ == 1)    Vin = VJt(:,J0,i);  else    Vin = VJt(:,1,i);  end  for (j = J0:-1:1)    Vout = imodwtj(WJt(:,j,i), Vin, ht, gt, j);    Vin = Vout;   end    X(:,i) = Vout(1:N);    end    return