Table 4 Total number of arithmetic operations required to compute the SRFFT_pruning, SRFFT_{pruning-time-shift}, and DFT_COMM algorithms

SRFFT_pruning

\( 6\left\{{\displaystyle \sum_{k=1}^d\left[{N_B}_{(k)}{N_W}_{(k)}\right]}\right.+\left.\frac{1}{2}\left({N_B}_{\left(d+1\right)}{N_W}_{\left(d+1\right)}\right)\right\}+2\left\{N\cdot d+{\displaystyle \sum_{k=0}^{r-\left(d+1\right)}\left[L{2}^k\right]}\right\} \)

–

SRFFT_{pruning-time-shift}

\( 6\left\{{\displaystyle \sum_{k=1}^{r-d}\left[{N_B}_{(k)}2L\right]+}\right.\left.{\displaystyle \sum_{k=r-d+1}^{r-1}\left\{{N_B}_{(k)}\left[{N_W}_{(k)}+2\right]\right\}}\right\}+2\left\{N\left(d-1\right)+N\right\} \)

–

DFT_COMM

6(L _o  − 1)(L _i  − 1) + 2L _o (L _i  − 1)

{(L _i  ≤ D _op )|(L _o  ≤ D _ip )} & (L _i  < 4)

(L _o  − 1)(2L _i  + 2) + 2(L _i  − 1) + (L _o  − 1)(4L _i  − 2)

{(L _i  ≤ D _op )|(L _o  ≤ D _ip )} & (L _i  ≥ 4)

6(L _i  − D _op )(D _ip  − 1) + D _ip D _op (4P log₂(P) − 6P + 8) + 6(L _o  − 1)(D _op  − 1) + 2L _o (D _op  − 1)

{(L _i  > D _op ) & (L _o  > D _ip )} & (D _op  < 4)

6(L _i  − D _op )(D _ip  − 1) + D _ip D _op (4P log₂(P) − 6P + 8) + (L _o  − 1)(2D _op  + 2) + 2(D _op  − 1) +

{(L _i  > D _op ) & (L _o  > D _ip )} & (D _op  ≥ 4)