Superposition frames for adaptive time-frequency analysis and fast reconstruction

TL;DR

This paper introduces superposition frames, a flexible family of adaptive time-frequency representations that enable fast, stable reconstruction and have practical applications like speech enhancement.

Contribution

The paper develops a new class of adaptive time-frequency representations called superposition frames, with properties ensuring efficient, invertible, and stable signal reconstruction.

Findings

Superposition frames allow fast overlap-add reconstruction.

They provide a stable, invertible signal representation.

Application to speech enhancement demonstrates practical utility.

Abstract

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.