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Table 2 Total number of arithmetic operations required to compute the input and output stages of DFTDIF−DIT−Pr and DFTDIT−DIF−Pr

From: Unified commutation-pruning technique for efficient computation of composite DFTs

Pruned decomposed transform

Corresponding term in (8)

Number of required real arithmetic operations

Limiting constraints

DFTDIF−DIT−Pr

OPERinput

6 (L i  − 1) (D ip  − 1)

–

 

OPERoutput

2L o (D op  − 1)

(L o  ≤ D ip )

  

2L o (D op  − 1) + 6 (L o  − D ip ) (D op  − 1)

(L o  > D ip ) & (D op  < 4)

  

(L o  − D ip ) (2D op  + 2) + 2D ip (D op  − 1) + (L o  − D ip ) (4D op  − 2)a

(L o  > D ip ) & (D op  ≥ 4)

DFTDIT−DIF−Pr

OPERinput

0

(L i  ≤ D op )

  

6 (L i  − D op ) (D ip  − 1)

(L i  > D op )

 

OPERoutput

6 (L o  − 1) (D op  − 1) + 2L o (D op  − 1)

(D op  < 4)

  

(L o  − 1) (2D op  + 2) + 2 (D op  − 1) + (L o  − 1) (4D op  − 2)a

(D op  ≥ 4)

  1. aNumber of required operations when the 2BF filtering method is employed [23, 24]