Journal ArticleDOI
Conjugate pair fast Fourier transform
I. Kamar,Y. Elcherif +1 more
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A new algorithm for the fast computation of the discrete Fourier transform (DFT) is introduced, called the conjugate pair FFT (CPFFT), which is used to compute a length-2m DFT.Abstract:
A new algorithm for the fast computation of the discrete Fourier transform is introduced. The algorithm, called the conjugate pair FFT (CPFFT), is used to compute a length-2m DFT. The number of multiplications and additions required by the CPFFT is less than that required by the SRFFT algorithm.read more
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Journal ArticleDOI
A Modified Split-Radix FFT With Fewer Arithmetic Operations
Steven G. Johnson,Matteo Frigo +1 more
TL;DR: A simple recursive modification of the split-radix algorithm is presented that computes the DFT with asymptotically about 6% fewer operations than Yavne, matching the count achieved by Van Buskirk's program-generation framework.
Fast fourier transform algorithms with applications
Shuhong Gao,Todd Mateer +1 more
TL;DR: This book presents an introduction to the principles of the fast Fourier transform, which covers FFTs, frequency domain filtering, and applications to video and audio signal processing.
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Type-II/III DCT/DST algorithms with reduced number of arithmetic operations
Xuancheng Shao,Steven G. Johnson +1 more
TL;DR: Algorithms are presented that achieve a lower count of real multiplications and additions than previously published algorithms, without sacrificing numerical accuracy, and it is shown that an additional N multiplications may be saved by a certain rescaling of the inputs or outputs.
Journal Article
A mathematical perspective
TL;DR: The author's perspective of his firsthand experience with Dr Merton Root and the methodology that Dr Root founded and the author's impressions of their impact on the profession are included.
Journal ArticleDOI
Type-IV DCT, DST, and MDCT algorithms with reduced numbers of arithmetic operations
Xuancheng Shao,Steven G. Johnson +1 more
TL;DR: These results are derived by considering the DCT to be a special case of a DFT of length 8N, with certain symmetries, and then pruning redundant operations from a recent improved fast Fourier transform algorithm (based on a recursive rescaling of the conjugate-pair split-radix algorithm).