Proceedings ArticleDOI
Fast transform digital filtering using non-diagonal spectral operators
H. Gethoffer
- Vol. 2, pp 356-359
TLDR
The step by step recursive analysis of cyclic convolution operators towards the associated diagonal spectral operators under the fast Fourier transform outlines a clear and deep insight into the algebraic structure of the intermediate operators and operations as well as into the mechanism of reducing redundant operations.Abstract:
The non-diagonal convolution theory is introduced as a normed commutative algebra based upon the isomorphism between time-discrete linear function spaces and arbitrary spectral spaces. The step by step recursive analysis of cyclic convolution operators towards the associated diagonal spectral operators under the fast Fourier transform outlines a clear and deep insight into the algebraic structure of the intermediate operators and operations as well as into the mechanism of reducing redundant operations. Finally, a new class of non-diagonal fast convolution algorithms for pipelined transforms and for the enhanced applicability of residue arithmetic in finite rings is presented.read more
Citations
More filters
Proceedings ArticleDOI
On complexity of fast convolution algorithms
TL;DR: It is shown that sequential complexity will decrease whereas parallel complexity will increase, and the reduction of the last transform step is resulting in an improved performance of fast transform filter algorithms, especially when the transform size is of moderate small size.
References
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Fast Convolution using fermat number transforms with applications to digital filtering
R. Agarwal,C.S. Burrus +1 more
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Journal Article
Fast convolution using Fermat number transforms with applications to digital filtering
TL;DR: The structure of transforms having the convolution property is developed and an implementation on the IBM 370/155 is presented and compared with the fast Fourier transform (FFT) showing a substantial improvement in efficiency and accuracy.
Journal ArticleDOI
Block realization of digital filters
TL;DR: In this article, different forms of block recursive digital filters are formulated using a matrix representation of convolution, and the multiplication efficiencies are calculated and compared, showing that the block realization can become more efficient for filters with orders exceeding approximately 25.
Journal ArticleDOI
Algebraic theory of finite fourier transforms
TL;DR: Both the Cooley-Tukey and Good algorithms are induced by a single functional congruence, the solutions to which define all algorithms of the Fast Fourier Transform type.