Quilted Gabor frames - a new concept for adaptive time-frequency representation

TL;DR

This paper introduces quilted frames, a novel adaptive time-frequency representation method that constructs frames directly in the time-frequency domain, enabling signal analysis tailored to local signal properties while ensuring reconstructability.

Contribution

The paper presents the concept of quilted frames, allowing for adaptive time-frequency analysis directly in the domain, which is a significant advancement over traditional fixed Gabor or wavelet frames.

Findings

Validity of the frame property is established for specific cases.

The Bessel property is proved in general settings.

Strategies for signal reconstruction and numerical simulations are provided.

Abstract

Certain signal classes such as audio signals call for signal representations with the ability to adapt to the signal's properties. In this article we introduce the new concept of quilted frames, which aim at adaptivity in time-frequency representations. As opposed to Gabor or wavelet frames, this new class of frames allows for the adaptation of the signal analysis to the local requirements of signals under consideration. Quilted frames are constructed directly in the time-frequency domain in a signal-adaptive manner. Validity of the frame property guarantees the possibility to reconstruct the original signal. The frame property is shown for specific situations and the Bessel property is proved for the general setting. Strategies for reconstruction from coefficients obtained with quilted Gabor frames and numerical simulations are provided as well.