Probabilistic complexity analysis for a class of approximate DFT algorithms

Winograd, Joseph M.; Nawab, S. Hamid

doi:10.1007/bf00925499

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Cited by 4 publications

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“…Instead, since the error will depend on the complexity of the signal, it would be of interest to explore a probabilistic approach, cf. Winograd and Nawab [28], to predict the signal dependent algorithmic complexity in an adaptive manner.…”

Section: Conclusion and Further Workmentioning

confidence: 99%

On the Equivalence Between a Minimal Codomain Cardinality Riesz Basis Construction, a System of Hadamard–Sylvester Operators, and a Class of Sparse, Binary Optimization Problems

Nelson

2014

IEEE Trans. Signal Process.

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Piecewise, low-order polynomial, Riesz basis families are constructed such that they share the same coefficient functionals of smoother, orthonormal bases in a localized indexing subset. It is shown that a minimal cardinality basis codomain can be realized by inducing sparsity, via regularization, in the distributional derivatives of the basis functions and that the optimal construction can be found numerically by constrained binary optimization over a suitably large dictionary. Furthermore, it is shown that a subset of these solutions are equivalent to a specific, constrained analytical solution, derived via Sylvester-type Hadamard operators.

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Section: Conclusion and Further Workmentioning

confidence: 99%