Strategies for Sparsity-based Time-Frequency Analyses
type: CreativeWork
description: Nonstationary signals are widely observed in many real-world applications, e.g., radar, sonar, radio astronomy, communication, acoustics, and vibration applications. Joint time-frequency (TF) domain representations provide a time-varying spectrum for their analyses, discrimination, and classifications. Nonstationary signals commonly exhibit sparse occupancy in the TF domain. In this dissertation, we incorporate such sparsity to enable robust TF analysis in impaired observing environments. In practice, missing data samples frequently occur during signal reception due to various reasons, e.g., propagation fading, measurement obstruction, removal of impulsive noise or narrowband interference, and intentional undersampling. Missing data samples in the time domain lend themselves to be missing entries in the instantaneous autocorrelation function (IAF) and induce artifacts in the TF representation (TFR). Compared to random missing samples, a more realistic and more challenging problem is the existence of burst missing data samples. Unlike the effects of random missing samples, which cause the artifacts to be uniformly spread over the entire TF domain, the artifacts due to burst missing samples are highly localized around the true instantaneous frequencies, rendering extremely challenging TF analyses for which many existing methods become ineffective. In this dissertation, our objective is to develop novel signal processing techniques that offer effective TF analysis capability in the presence of burst missing samples. We propose two mutually related methods that recover missing entries in the IAF and reconstruct high-fidelity TFRs, which approach full-data results with negligible performance loss. In the first method, an IAF slice corresponding to the time or lag is converted to a Hankel matrix, and its missing entries are recovered via atomic norm minimization. The second method generalizes this approach to reduce the effects of TF crossterms. It considers an IAF patch,…
abstract: Nonstationary signals are widely observed in many real-world applications, e.g., radar, sonar, radio astronomy, communication, acoustics, and vibration applications. Joint time-frequency (TF) domain representations provide a time-varying spectrum for their analyses, discrimination, and classifications. Nonstationary signals commonly exhibit sparse occupancy in the TF domain. In this dissertation, we incorporate such sparsity to enable robust TF analysis in impaired observing environments. In practice, missing data samples frequently occur during signal reception due to various reasons, e.g., propagation fading, measurement obstruction, removal of impulsive noise or narrowband interference, and intentional undersampling. Missing data samples in the time domain lend themselves to be missing entries in the instantaneous autocorrelation function (IAF) and induce artifacts in the TF representation (TFR). Compared to random missing samples, a more realistic and more challenging problem is the existence of burst missing data samples. Unlike the effects of random missing samples, which cause the artifacts to be uniformly spread over the entire TF domain, the artifacts due to burst missing samples are highly localized around the true instantaneous frequencies, rendering extremely challenging TF analyses for which many existing methods become ineffective. In this dissertation, our objective is to develop novel signal processing techniques that offer effective TF analysis capability in the presence of burst missing samples. We propose two mutually related methods that recover missing entries in the IAF and reconstruct high-fidelity TFRs, which approach full-data results with negligible performance loss. In the first method, an IAF slice corresponding to the time or lag is converted to a Hankel matrix, and its missing entries are recovered via atomic norm minimization. The second method generalizes this approach to reduce the effects of TF crossterms. It considers an IAF patch,…
author: Zhang, Shuimei
language: eng
keywords: Electrical engineering, Burst missing samples, Crossterm mitigation, Deep neural network, Low-rank structured matrix completion, Nonstationary signal, Time-frequency analysis
license: http://rightsstatements.org/vocab/InC/1.0/
date published: 2021
date modified: 2026-07-27T21:20:03Z
provider: Temple University
publisher: Networked Digital Library of Theses and Dissertations
type: WebPage
source organization: Temple University. Libraries

PropertyValue
property ID: Handle
value: http://hdl.handle.net/20.500.12613/6457