Signal and Image Processing with Sinlets

TL;DR

This paper introduces sinlets, a new family of localized orthonormal bases for signal and image processing, offering advantages over Fourier transforms for analyzing time-varying frequency signals.

Contribution

The paper develops and characterizes sinlets, a novel basis related to harmonic oscillator solutions, suitable for efficient representation of transient signals in various applications.

Findings

Sinlets provide accurate signal representation with real-valued coefficients.

They are well-suited for analyzing signals with changing frequency content.

Sinlets can be extended to multi-dimensional bases for image analysis.

Abstract

This paper presents a new family of localized orthonormal bases - sinlets - which are well suited for both signal and image processing and analysis. One-dimensional sinlets are related to specific solutions of the time-dependent harmonic oscillator equation. By construction, each sinlet is infinitely differentiable and has a well-defined and smooth instantaneous frequency known in analytical form. For square-integrable transient signals with infinite support, one-dimensional sinlet basis provides an advantageous alternative to the Fourier transform by rendering accurate signal representation via a countable set of real-valued coefficients. The properties of sinlets make them suitable for analyzing many real-world signals whose frequency content changes with time including radar and sonar waveforms, music, speech, biological echolocation sounds, biomedical signals, seismic acoustic waves, and signals employed in wireless communication systems. One-dimensional sinlet bases can be used to construct two- and higher-dimensional bases with variety of potential applications including image analysis and representation.