求各位大神帮看下这段s逆变换matlab code !!!!

weiweiamazon

最近刚开始学习s变换，这是从网上下载的一段Stockwell写的逆变换matlab代码，里面注释较多，实际其实有10行左右。想请教各位大神为什么要分情况讨论有奇数个点和偶数个点？if rem(ntimes ,2) ~= 0 ？
非常感谢！

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);