Module 9 : Numerical Relaying II : DSP Perspective

Lecture 35 : Computation of Phasor from Discrete Fourier Transform

35.2

Phase Computation using DFT (contd..)

   
 

In the computation of phasor, we would not like this phasor rotation to occur due to DFT phase shifting. This can be avoided if we modify equation (6) and (7). Replace = 0 by = , in the lower limit and = N + - 1 in the upper limit, we get
     
  Where
  (10)
    (11)
 

Substituting in equation (10), we get
     
  for m = 1;  
 
  for m = 1;
  Hence,
  Thus, we conclude that artificial rotation induced in phasor computation by using DFT equations can be eliminated by appropriately modifying the offset in the summation index of DFT equation.
35.3 Full Cycle Recursive DFT
  From equation (10) and (11), we have
 
  and
 
 
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