IEEE Transactions on Computers
Design & analysis of fault tolerant digital systems
Design & analysis of fault tolerant digital systems
Computational frameworks for the fast Fourier transform
Computational frameworks for the fast Fourier transform
Generalized Algorithm-Based Fault Tolerance: Error Correction via Kalman Estimation
IEEE Transactions on Computers
An Adaptation of the Fast Fourier Transform for Parallel Processing
Journal of the ACM (JACM)
Fast Transforms: Algorithms, Analyses, Applications
Fast Transforms: Algorithms, Analyses, Applications
Algorithm-Based Fault Tolerance for FFT Networks
IEEE Transactions on Computers
An Efficient Algorithm-Based Concurrent Error Detection for FFT Networks
IEEE Transactions on Computers
A Novel Concurrent Error Detection Scheme for FFT Networks
IEEE Transactions on Parallel and Distributed Systems
Kronecker Product Factorization of the FFT Matrix
IEEE Transactions on Computers
Fast Algorithms for the 2-D Discrete Cosine Transform
IEEE Transactions on Computers
One- and two-dimensional constant geometry fast cosine transformalgorithms and architectures
IEEE Transactions on Signal Processing
Concurrent Error Detection in Wavelet Lifting Transforms
IEEE Transactions on Computers
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Abstract: Discrete fast unitary transform algorithms, of which the fast Fourier transform (FFT) and fast discrete Cosine transform (DCT) are practical examples, are highly susceptible to temporary calculation failures because of their interconnected computational flows. Many error detection techniques for FFT algorithms have been reported, but fault tolerance issues for other important transforms have not been addressed as vigorously. A general design and analysis approach for all fast unitary transforms is presented. It relies on fundamental linear algebra methods coupled with associated dual space representations that are used to define an equal-sized group of dual space basis vectors on which practical parity weighting functions may be evaluated. An iterative design approach leads to complete single error detection capabilities. FFT and fast DCT examples are given.