Some FFT Algorithms for Small-Length Real-Valued Sequences
Dorota Majorkowska-Mech, Aleksandr Cariow
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.
Topics & Concepts
Split-radix FFT algorithmFast Fourier transformPrime-factor FFT algorithmAlgorithmComputer scienceNotationCyclotomic fast Fourier transformRader's FFT algorithmTwiddle factorDiscrete Fourier transform (general)MathematicsArithmeticFourier transformFourier analysisShort-time Fourier transformMathematical analysisDigital Filter Design and ImplementationNumerical Methods and AlgorithmsImage and Signal Denoising Methods