Some FFT Algorithms for Small-Length Real-Valued Sequences

Abstract

This paper proposes fast algorithms for computing the discrete Fourier transform for real-valued sequences of lengths from 3 to 9. Since calculating the real-valued DFT using the complex-valued FFT is redundant regarding the number of needed operations, the developed algorithms do not operate on complex numbers. The algorithms are described in matrix–vector notation and their data flow diagrams are shown.

Keywords

• discrete Fourier transform
• fast algorithm
• matrix–vector notation