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) |