1. Comparison
=====

Procedure taken to receive results:
  1. Generate amp_corr.dat using the TISEAN package 'corr' with the call: 
       'corr amplitude.dat -D5000 -o "amp_corr.dat"'
  2. Generate similar autocorelation data using 
        'load amplitude.dat; [a,b] = xcorr(amplitude,5000, 'coeff');'
     
     Then to save the data you can use:
        'idx = [rows(amplitude):2*rows(amplitude)-1]; xcorr_res = a(idx); save "xcorr_res.dat" xcorr_res'

There is a strong difference in the data. This might be because of the different methods used in both cases (as explained further in the methods used Section 2. Methods). Because of those differences the amplitudes of the data generated using 'xcorr' from 'signal' decreases linearly. Thus to compare the data the oscillation amplitude of the data generated by 'xcorr' must be amplified. This linear decrease was not proven but observed on the 'amplitude.dat' data. 

When a linear correction is applied:

    'mult = rows (amplitude) ./ (rows (amplitude) - [0:rows(amplitude)-1]); xcorr_tisean_res = mult .* xcorr_res'

The resultant xcorr_tisean_res is close to the TISEAN 'corr' function.

The data is very close at the beginning but towards the end it beginns to vary until it reaches about 3% for 'amplitude.dat'. This is most likely because towards the end the data ends, so there is less data to generate a proper autocorrelation.

Similar results were achieved when using 'amp_ar.dat' although the difference at its peak was smaller than 1.5%. 


2. Methods
=====
*  The way 'corr' determines the autocorrelation of the data is using an estimation procedure described here:
http://en.wikipedia.org/wiki/Autocorrelation#Estimation

*  The function 'xcorr' from package 'signal' works usingthe FFT (Fast Fourier Transform) method. It is described here:
http://en.wikipedia.org/wiki/Autocorrelation#Efficient_computation
