The tensor product: a mathematical programming language for FFTs and other fast DSP operations
- 1 January 1992
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in IEEE Signal Processing Magazine
- Vol. 9 (1) , 40-48
- https://doi.org/10.1109/79.109206
Abstract
The use of the tensor product as a tool for modeling and developing digital signal processing algorithms is discussed. A precise mathematical definition of the tensor product is established along with several important properties. Special tensor matrices suited for implementation on various computer architectures are then identified. The notion of the stride permutation matrix is introduced as a method of modeling operand addressing. An important connection between tensor matrices and stride permutations is made explicit. By identifying particular tensor matrices suited for implementation on a given machine the tensor product has been transformed from a mathematical convenience into an extremely useful tool for matching algorithms to computer architectures. Several design examples in which a tensor matrix multiplication is implemented on several radically different types of computer architectures are presented.Keywords
This publication has 9 references indexed in Scilit:
- Discrete Fast fourier Transorm Algorithms: A Tutorial SurveyPublished by Elsevier ,1991
- A methodology for designing, modifying, and implementing Fourier transform algorithms on various architecturesCircuits, Systems, and Signal Processing, 1990
- Modified Winograd FFT algorithm and its variants for transform size N = pk and their implementationsAdvances in Applied Mathematics, 1989
- Algorithms for Discrete Fourier Transform and ConvolutionPublished by Springer Nature ,1989
- On computing the split-radix FFTIEEE Transactions on Acoustics, Speech, and Signal Processing, 1986
- Self-sorting mixed-radix fast Fourier transformsJournal of Computational Physics, 1983
- An algorithm for computing the mixed radix fast Fourier transformIEEE Transactions on Audio and Electroacoustics, 1969
- An Adaptation of the Fast Fourier Transform for Parallel ProcessingJournal of the ACM, 1968
- An algorithm for the machine calculation of complex Fourier seriesMathematics of Computation, 1965