function [SJt, att] = imodwt_smooth(VJt, wtfname, J0)% imodwt_smooth -- Calculate smooths at J0 level via inverse maximal overlap discrete wavelet transform (IMODWT).%%****f* wmtsa.dwt/imodwt_smooth%% NAME%   imodwt_smooth -- Calculate smooths at J0 level via inverse maximal overlap discrete wavelet transform (IMODWT).%% SYNOPSIS%   [SJt, att] = imodwt_smooth(VJt, wtfname, J0)%% INPUTS%   VJt         =  Nx1 vector of MODWT scaling coefficients at J0 level.%   wtfname      =  string containing name of a WMTSA-supported MODWT wavelet %                   filter.%% OUTPUT%   SJOt         =  vector of reconstituted smoothed data series.%   att          =  structure containing IMODWT transform attributes%   J0           =  number of levels of partial decomposition.%% SIDE EFFECTS%   1.  wtfname is a WMTSA-supported MODWT wavelet filter; otherwise error.%% DESCRIPTION%%% EXAMPLE%   [SJt, att] = imodwt_smooth(VJt, 'la8');%%% NOTES%%% ALGORITHM%   See pages 177-179 of WMTSA for description of Pyramid Algorithm for%   the inverse MODWT multi-resolution analysis.%% REFERENCES%   Percival, D. B. and A. T. Walden (2000) Wavelet Methods for%   Time Series Analysis. Cambridge: Cambridge University Press.%% SEE ALSO%   imodwtj, imodwt, imodwt_details, modwt_filter, modwt%% AUTHOR%   Charlie Cornish%% CREATION DATE%   2003-05-01%% COPYRIGHT%%% REVISION%   $Revision: 612 $%%***% $Id: imodwt_smooth.m 612 2005-10-28 21:42:24Z ccornish $  usage_str = ['Usage:  [SJt, att] = ', mfilename, ...             '(VJt, wtfname, J0)'];  %%  Check input arguments and set defaults.error(nargerr(mfilename, nargin, [3:3], nargout, [0:2], 1, usage_str, 'struct'));%% Get a valid wavelet transform filter coefficients struct.if (ischar(wtfname))  try    [wtf_s] = modwt_filter(wtfname);  catch    rethrow(lasterror);  endelse  error('WMTSA:invalidWaveletTransformFilter', ...        encode_errmsg('WMTSA:invalidWaveletTransformFilter', wmtsa_err_table, 'wtf'));endwtfname = wtf_s.Name;L = wtf_s.L;gt = wtf_s.g;ht = wtf_s.h;N = length(VJt);zeroj =  zeros(N, 1);SJt = zeros(N, 1);Vin = VJt;for (j = J0:-1:1)  Vout = imodwtj(zeroj, Vin, ht, gt, j);  Vin = Vout; endSJt = Vout;SJt = SJt(:);    att.Transform = 'IMODWT';att.WTF = wtfname;att.N = N;att.J0 = J0;return