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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−2−n+1a

Canonic ROFFT

\(\frac {N}{2}-1\)

\(\frac {N}{4}\text {log}_{2}N-\frac {N}{2}\)

2n−2−n+1a

  1. aWhen n≥2, there will also be n−2 multiplications of \(\sqrt {2}\) in the flow graph