function svar = modwt_wavelet_sample_variance(WJ, VJ0, X)% modwt_wavelet_sample_variance -- Compute sample variance from MODWT wavelet decomposition and orignal data series.%% Usage:%   s2 = wavelet_sample_variance(WJ, VJ0, X)%% Inputs:%   WJ           =  NxJ array of MODWT wavelet coefficents%   VJ0          =  Nx1 vector of MODWT scaling coefficients%   X            =  original data series%% Outputs:%   svar         = sample variance computed from wavelet decomposition.%% SideEffects:%%% Description:%%% Examples:%%% Notes:%%% Algorithm:%   See equations 104b pg. 104 and 171a pg. 171 of WMTSA.%% See Also:%%% References%   Percival, Donald B., and Andrew T. Walden (2000). Wavelet Methods %     for Time Series Analysis, Cambridge University Press.% $Id: modwt_wavelet_sample_variance.m 612 2005-10-28 21:42:24Z ccornish $%% Author:%   Charlie Cornish%% Date:%   2003-04-23%% Credits:%%  global VERBOSE;  usage_str = ['Usage:  [svar]  = ', mfilename, ...               '(WJ, VJ0, X)'];  %%  Check input arguments and set defaults.  error(nargerr(mfilename, nargin, [3:3], nargout, [0:1], 1, usage_str, 'struct'));  N = length(X);    svar = ( sum(sum(WJ.^2)) / N ) + ...         ( sum(VJ0.^2)     / N ) - ...         ( mean(X).^2 );  return