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Table 5 Performance comparison for N=2n-point FFT algorithms

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−2n+1a
Canonic ROFFT \(\frac {N}{2}-1\) \(\frac {N}{4}\text {log}_{2}N-\frac {N}{2}\) 2n−2n+1a
  1. aWhen n≥2, there will also be n−2 multiplications of \(\sqrt {2}\) in the flow graph