Table 1 Energy consumed for N-point FFT vs.

Number of butterflies

2

1

1

Number of stages

log₂(N)

log₄(N)

log₈(N)

Number of butterflies

operations/stage

$\frac{N}{2}$

$\frac{N}{4}$

$\frac{N}{8}$

Number of clock

cycles/butterflies

1

1

2

Total number of clock

cycles for N -point FFT

$\frac{N}{4}{log}_2\left(N\right)\left(\frac{N}{4}\right)\left(x\right)$

$\frac{N}{4}{log}_4\left(N\right)\left(\frac{N}{4}\right)\left(\frac{x}{2}\right)$

$\frac{N}{4}{log}_8\left(N\right)\times 2\left(\frac{N}{4}\right)\left(\frac{x}{3}\right)$

Normalized power

2

3

7

Power efficiency

0.5 × N × x

0.375 × N × x

0.43 × N × x

As N = 2^x