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On multitapers in time-frequency reassignment

Åkesson, Maria LU (2024) In Licentiate Thesis in Mathematical Sciences
Abstract
Time-varying signals, such as sound waves, low-frequency vibrations from the earth, or electrical impulses in the human body, are often non-stationary, meaning their characteristics change over time. Because of this, standard spectral analysis methods, which assume stationary signals, cannot be used for analyzing such signals, as they discard the time-varying dynamics. This necessitates methods for joint time-frequency (TF) analysis, which is the topic of this licentiate thesis.

In particular, this thesis considers the reassignment technique, a post-processing procedure that relocates mass in a bilinear time-frequency representation to the signal's instantaneous frequency and group delay, improving the localization of the signal.... (More)
Time-varying signals, such as sound waves, low-frequency vibrations from the earth, or electrical impulses in the human body, are often non-stationary, meaning their characteristics change over time. Because of this, standard spectral analysis methods, which assume stationary signals, cannot be used for analyzing such signals, as they discard the time-varying dynamics. This necessitates methods for joint time-frequency (TF) analysis, which is the topic of this licentiate thesis.

In particular, this thesis considers the reassignment technique, a post-processing procedure that relocates mass in a bilinear time-frequency representation to the signal's instantaneous frequency and group delay, improving the localization of the signal. Reassignment generally works well for localizing slowly varying long-duration chirps but fails to enhance short-duration transients. Additionally, the method is sensitive to noise.

Four papers are included in this thesis. In Paper I, the reassigned time-frequency representation is shown to become more robust to noise by including multitapers in the reassignment. Furthermore, in Paper II, the same method is shown to enhance short-duration transients in addition to long-duration chirps. This makes the reassigned multitaper spectrogram suitable for exploratory analysis of signals containing a mixture of chirps and transients, which is illustrated on bat-, dolphin- and bird-audio data.

Paper III and IV focus on estimating the phase delay between two oscillating transient signals, which is of interest in, for instance, spatiotemporal decoding in neurophysiology. In Paper III we argue how reassignment of the cross-spectrogram can be constructed for fast and precise phase delay estimation between two transients. In Paper IV, improvements to the phase-estimation procedure in paper III are made by incorporating multitapers in the reassignment. Examples of the phase estimates on real data from evoked visual potential experiments are included in the papers. (Less)
Please use this url to cite or link to this publication:
author
supervisor
organization
publishing date
type
Thesis
publication status
published
subject
keywords
Instantaneous frequency, Gabor atom, Spectrogram
in
Licentiate Thesis in Mathematical Sciences
issue
2024:5
pages
103 pages
publisher
Lunds Universitet, Centre for Mathematical Sciences
ISSN
1404-028X
ISBN
978-91-8104-263-4
978-91-8104-262-7
language
English
LU publication?
yes
id
b4ade904-6f6c-4fa7-b8ec-706cff828f30
date added to LUP
2024-11-08 11:01:49
date last changed
2025-12-05 10:03:31
@misc{b4ade904-6f6c-4fa7-b8ec-706cff828f30,
  abstract     = {{Time-varying signals, such as sound waves, low-frequency vibrations from the earth, or electrical impulses in the human body, are often non-stationary, meaning their characteristics change over time. Because of this, standard spectral analysis methods, which assume stationary signals, cannot be used for analyzing such signals, as they discard the time-varying dynamics. This necessitates methods for joint time-frequency (TF) analysis, which is the topic of this licentiate thesis. <br/><br/>In particular, this thesis considers the reassignment technique, a post-processing procedure that relocates mass in a bilinear time-frequency representation to the signal's instantaneous frequency and group delay, improving the localization of the signal. Reassignment generally works well for localizing slowly varying long-duration chirps but fails to enhance short-duration transients. Additionally, the method is sensitive to noise.<br/><br/>Four papers are included in this thesis. In Paper I, the reassigned time-frequency representation is shown to become more robust to noise by including multitapers in the reassignment. Furthermore, in Paper II, the same method is shown to enhance short-duration transients in addition to long-duration chirps. This makes the reassigned multitaper spectrogram suitable for exploratory analysis of signals containing a mixture of chirps and transients, which is illustrated on bat-, dolphin- and bird-audio data. <br/><br/>Paper III and IV focus on estimating the phase delay between two oscillating transient signals, which is of interest in, for instance, spatiotemporal decoding in neurophysiology. In Paper III we argue how reassignment of the cross-spectrogram can be constructed for fast and precise phase delay estimation between two transients. In Paper IV, improvements to the phase-estimation procedure in paper III are made by incorporating multitapers in the reassignment. Examples of the phase estimates on real data from evoked visual potential experiments are included in the papers.}},
  author       = {{Åkesson, Maria}},
  isbn         = {{978-91-8104-263-4}},
  issn         = {{1404-028X}},
  keywords     = {{Instantaneous frequency; Gabor atom; Spectrogram}},
  language     = {{eng}},
  month        = {{11}},
  note         = {{Licentiate Thesis}},
  number       = {{2024:5}},
  publisher    = {{Lunds Universitet, Centre for Mathematical Sciences}},
  series       = {{Licentiate Thesis in Mathematical Sciences}},
  title        = {{On multitapers in time-frequency reassignment}},
  url          = {{https://lup.lub.lu.se/search/files/199300595/e-spik_ex_kesson.pdf}},
  year         = {{2024}},
}