Multiplicative complexity, convolution, and the DFT
Multiplicative complexity, convolution, and the DFT
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Numerical recipes in C (2nd ed.): the art of scientific computing
Numerical recipes in C (2nd ed.): the art of scientific computing
A polynomial approach to linear algebra
A polynomial approach to linear algebra
Numerical Analysis: A fast fourier transform algorithm for real-valued series
Communications of the ACM
ICASSP '96 Proceedings of the Acoustics, Speech, and Signal Processing, 1996. on Conference Proceedings., 1996 IEEE International Conference - Volume 03
Library generation for linear transforms
Library generation for linear transforms
A comparative study of different FFT architectures for software defined radio
SAMOS'07 Proceedings of the 7th international conference on Embedded computer systems: architectures, modeling, and simulation
A Modified Split-Radix FFT With Fewer Arithmetic Operations
IEEE Transactions on Signal Processing
Prime-length real-valued polynomial residue division algorithms
IEEE Transactions on Signal Processing
The quick Fourier transform: an FFT based on symmetries
IEEE Transactions on Signal Processing
Algebraic Signal Processing Theory: Cooley–Tukey Type Algorithms for DCTs and DSTs
IEEE Transactions on Signal Processing
Algebraic Signal Processing Theory: 1-D Space
IEEE Transactions on Signal Processing - Part I
Algebraic Signal Processing Theory: Foundation and 1-D Time
IEEE Transactions on Signal Processing - Part I
Improved twiddle access for fast fourier transforms
IEEE Transactions on Signal Processing
A novel split-radix fast algorithm for 2-D discrete Hartley transform
IEEE Transactions on Circuits and Systems Part I: Regular Papers
Computer Generation of Hardware for Linear Digital Signal Processing Transforms
ACM Transactions on Design Automation of Electronic Systems (TODAES)
Parameterized micro-benchmarking: an auto-tuning approach for complex applications
Proceedings of the 9th conference on Computing Frontiers
When polyhedral transformations meet SIMD code generation
Proceedings of the 34th ACM SIGPLAN conference on Programming language design and implementation
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In this paper, we systematically derive a large class of fast general-radix algorithms for various types of real discrete Fourier transforms (real DFTs) including the discrete Hartley transform (DHT) based on the algebraic signal processing theory. This means that instead of manipulating the transform definition, we derive algorithms by manipulating the polynomial algebras underlying the transforms using one general method. The same method yields the well-known Cooley-Tukey fast Fourier transform (FFT) as well as general radix discrete cosine and sine transform algorithms. The algebraic approach makes the derivation concise, unifies and classifies many existing algorithms, yields new variants, enables structural optimization, and naturally produces a human-readable structural algorithm representation based on the Kronecker product formalism. We show, for the first time, that the general-radix Cooley-Tukey and the lesser known Bruun algorithms are instances of the same generic algorithm. Further, we show that this generic algorithm can be instantiated for all four types of the real DFT and the DHT.