From: Canonic FFT flow graphs for real-valued even/odd symmetric inputs
FFT algorithm | #Signal values at each stage | #Real butterfly operation | #Twiddle factor operations |
---|---|---|---|
Complex FFT | 2N | Nlog2 N | n×2n−1−2n+2 |
[6] DIF RFFT | ≥N | \(\left (\frac {N}{2}-1\right)\text {log}_{2}N+1\) | \(\left (n-\frac {7}{2}\right)\times 2^{n-2}+n-1\) |
[11] Canonic DIT RFFT | N | \(\frac {N}{2}\text {log}_{2}N-\frac {N}{2}+1\) | (n−3)×2n−2+1 |
[11] Canonic DIF RFFT | N | \(\frac {N}{2}\text {log}_{2}N-\frac {N}{2}+1\) | (n−4)×2n−2+n |
Canonic REFFT | \(\frac {N}{2}+1\) | \(\left (\frac {N}{4}+1\right)\text {log}_{2}N-\frac {N}{2}\) | 2n−2−n+1a |
Canonic ROFFT | \(\frac {N}{2}-1\) | \(\frac {N}{4}\text {log}_{2}N-\frac {N}{2}\) | 2n−2−n+1a |