On Wigner-Ville Spectra and the Unicity of Time-Varying Quantile-Based Spectral Densities
Stefan Birr, Holger Dette, Marc Hallin, Tobias Kley, Stanislav, Volgushev
TL;DR
This paper proves the uniqueness of a specific type of time-varying spectral density based on quantiles, using asymptotic analysis involving Wigner-Ville spectra.
Contribution
It establishes the unicity of the time-varying quantile-based spectrum through an asymptotic representation involving Wigner-Ville spectra.
Findings
Uniqueness of the spectrum is mathematically proven.
Asymptotic representation links quantile-based spectra to Wigner-Ville spectra.
Theoretical foundation for quantile-based spectral analysis is strengthened.
Abstract
The unicity of the time-varying quantile-based spectrum proposed in Birr et al. (2016) is established via an asymptotic representation result involving Wigner-Ville spectra.
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Taxonomy
TopicsMathematical Analysis and Transform Methods · Image and Signal Denoising Methods