Analyzing Chaos Systems and Fine Spectrum Sensing Using Detrended Fluctuation Analysis Algorithm

Algorithm 1

The DFA algorithm steps.

Step  1. Random walk calculation:

   for   (

    (the mean of the data series);

    ;

   end for

Step  2. Using the interval size , is divided to intervals

Step  3. for

    The fitting process is performed using polynomial function of order ;

   end for

Step  4. for

    for

    ; (detrended fluctuation signal)

    end for

   end for

Step  5. Root mean square (rms) calculation:

   for (

      ;

   end for

Step  6. Finding the relation between the fluctuation and the scale:

   for (

    repeat the steps from 1 to 5 (1~5)

   end for

   The power law relation: where