Two Families of Radix-2 FFT Algorithms With Ordered Input and Output Data

Two radix-2 families of fast Fourier transform (FFT) algorithms that have the property that both inputs and outputs are addressed in natural order are derived in this letter. The algorithms obtained have the same complexity that Cooley-Tukey radix-2 algorithms but avoid the bit-reversal ordering applied to the input. These algorithms can be thought as a variation of the radix-2 Cooley-Tukey ones.