function [ts] = inverse_st(st)
% Returns the inverse of the Stockwell Transform of the REAL_VALUED timeseries.
% Code by Robert Glenn Stockwell.
% Reference is "Localization of the Complex Spectrum: The S Transform"
% from IEEE Transactions on Signal Processing, vol. 44., number 4, April 1996, pages 998-1001.
%
%-------Inputs Needed------------------------------------------------
%  
%  S-Transform matrix created by the st.m function
%-------Optional Inputs ------------------------------------------------
% none
%-------Outputs Returned------------------------------------------------
%
% ts     -a REAL-VALUED time series
%--------Additional details-----------------------
%   Copyright (c) by Bob Stockwell
%   $Revision: 1.0 $  $Date: 2004/10/10  $

% sum over time to create the FFT spectrum for the positive frequencies
stspe = sum(st,2);

% get st matrix dimensions 
[nfreq,ntimes] = size(st);
if rem(ntimes ,2) ~= 0
    % odd number of points, so nyquist point is not aliased, so concatenate
    % the reversed spectrum to create the negative frequencies
    % drop the DC value
    negspe = fliplr(stspe(2:nfreq)');
else
     % even number of points
     % therefore drop the first point (DC) and the last point (aliased nyqusit freq)
     negspe = fliplr(stspe(2:nfreq-1)');
end

% using symmetry of FFT spectrum of a real signal, recreate the negative frequencies from the positie frequencies
 fullstspe = [conj(stspe')  negspe];    

% the time series is the inverse fft of this
ts = ifft(fullstspe);
% and take the real part, the imaginary part will be zero.
ts = real(ts);