Superposition frames for adaptive time-frequency analysis and fast reconstruction
For signal processing researchers, this provides a theoretically grounded adaptive time-frequency analysis method with efficient reconstruction, though the speech enhancement example is preliminary.
The authors introduce superposition frames, a family of adaptive linear time-frequency representations that enable fast overlap-add reconstruction, unlike many existing adaptive methods. They prove numerical stability and invertibility, and demonstrate potential in speech enhancement.
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.