title: calculate discrete S transform for given discrete time series
body: <p>let us consider following  Page :</p>
  
  <p><a href="http://djj.ee.ntu.edu.tw/S_Transform.pdf" rel="nofollow noreferrer">http://djj.ee.ntu.edu.tw/S_Transform.pdf</a></p>
  
  <p>paragraph  2.3 The Discrete S Transform</p>
  
  <p>let say that we have  sampled version of signal  x, and given sampling frequency fs,i have calculated discrete Fourier transform using following code</p>
  
  <pre><code>function y=DFT(x);
  N=length(x);
  D=zeros(N,N);
  for k=1:N
      for n=1: N
          D(k,n)=exp((-j*(k-1)*2*pi*(n-1))/N);
      end
  end
  y=D*x'/N;
  end
  </code></pre>
  
  <p>and started to estimate  discrete  S transform</p>
  
  <pre><code>function [S]=discrete_s_transform(x,fs);
  %compute discrete  s transform
  %fs-sampling frequency 
  N=length(x); % length of signal
  T=1/fs; % sampling period
  Y=DFT(X);
  </code></pre>
  
  <p>how can i continue  related to this part ?
  <img src="https://i.stack.imgur.com/tGcaC.png" alt="enter image description here"></p>
  
  <p>clearly loops are not problem to implement,just they go  from 1 to N instead of 0 to N-1 because of matlab vectors are 1 based,but what about main code?multiplication to exponential? coudl you please help me to  finish S transform ?</p>