Mathematics – Numerical Analysis
Scientific paper
2009-06-29
IEEE Transactions on Signal Processing, vol. 58, pp. 2581-2596, 2010
Mathematics
Numerical Analysis
16 pages, 6 figures; revised version
Scientific paper
10.1109/TSP.2010.2041604
In this article we introduce a broad family of adaptive, linear time-frequency representations termed superposition frames, and show that they admit desirable fast overlap-add reconstruction properties akin to standard short-time Fourier techniques. This approach stands in contrast to many adaptive time-frequency representations in the extant literature, which, while more flexible than standard fixed-resolution approaches, typically fail to provide efficient reconstruction and often lack the regular structure necessary for precise frame-theoretic analysis. Our main technical contributions come through the development of properties which ensure that this construction provides for a numerically stable, invertible signal representation. Our primary algorithmic contributions come via the introduction and discussion of specific signal adaptation criteria in deterministic and stochastic settings, based respectively on time-frequency concentration and nonstationarity detection. We conclude with a short speech enhancement example that serves to highlight potential applications of our approach.
Basu Prabahan
Rudoy Daniel
Wolfe Patrick J.
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