Frame Theory for Signal Processing in Psychoacoustics

Abstract

This review chapter aims to strengthen the link between frame theory and signal processing tasks in psychoacoustics. On the one side, the basic concepts of frame theory are presented and some proofs are provided to explain those concepts in some detail. The goal is to reveal to hearing scientists how this mathematical theory could be relevant for their research. In particular, we focus on frame theory in a filter bank approach, which is probably the most relevant view-point for audio signal processing. On the other side, basic psychoacoustic concepts are presented to stimulate mathematicians to apply their knowledge in this field.

References in corpus (3)

• Structure of nonstationary Gabor frames and their dual systems
• Efficient algorithms for discrete Gabor transforms on a nonseparable lattice
• A Perceptually Motivated Filter Bank with Perfect Reconstruction for Audio Signal Processing

Cited by in corpus (7)

• Generalized frame operator, lower semi-frames and sequences of translates
• U-cross Gram matrices and their invertibility
• Instabilities in Convnets for Raw Audio
• Localization of the spectra of dual frames multipliers
• Using B-spline frames to approximate solutions of acoustic scattering problems
• On the relation of the frame-related operators of fusion frame systems
• On some dual frames multipliers with at most countable spectra