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Thesis/Dissertation
Date
2022
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Electrical and Computer Engineering
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http://dx.doi.org/10.34944/dspace/7753
Abstract
Non-stationary signals, particularly frequency modulated (FM) signals which arecharacterized by their time-varying instantaneous frequencies (IFs), are fundamental
to radar, sonar, radio astronomy, biomedical applications, image processing, speech
processing, and wireless communications. Time-frequency (TF) analyses of such signals
provide two-dimensional mapping of time-domain signals, and thus are regarded
as the most preferred technique for detection, parameter estimation, analysis and
utilization of such signals.
In practice, these signals are often received with compressed measurements as a
result of either missing samples, irregular samplings, or intentional under-sampling of
the signals. These compressed measurements induce undesired noise-like artifacts in
the TF representations (TFRs) of such signals. Compared to random missing data,
burst missing samples present a more realistic, yet a more challenging, scenario for
signal detection and parameter estimation through robust TFRs. In this dissertation,
we investigated the effects of burst missing samples on different joint-variable domain
representations in detail.
Conventional TFRs are not designed to deal with such compressed observations.
On the other hand, sparsity of such non-stationary signals in the TF domain facilitates
utilization of sparse reconstruction-based methods. The limitations of conventional
TF approaches and the sparsity of non-stationary signals in TF domain motivated us
to develop effective TF analysis techniques that enable improved IF estimation of such
signals with high resolution, mitigate undesired effects of cross terms and artifacts
and achieve highly concentrated robust TFRs, which is the goal of this dissertation.
In this dissertation, we developed several TF analysis techniques that achieved
the aforementioned objectives. The developed methods are mainly classified into two
three broad categories: iterative missing data recovery, adaptive local filtering based TF approach, and signal stationarization-based approaches. In the first category,
we recovered the missing data in the instantaneous auto-correlation function (IAF)
domain in conjunction with signal-adaptive TF kernels that are adopted to mitigate
undesired cross-terms and preserve desired auto-terms. In these approaches, we took
advantage of the fact that such non-stationary signals become stationary in the IAF
domain at each time instant. In the second category, we developed a novel adaptive
local filtering-based TF approach that involves local peak detection and filtering of
TFRs within a window of a specified length at each time instant. The threshold for
each local TF segment is adapted based on the local maximum values of the signal
within that segment. This approach offers low-complexity, and is particularly
useful for multi-component signals with distinct amplitude levels. Finally, we developed
knowledge-based TFRs based on signal stationarization and demonstrated
the effectiveness of the proposed TF techniques in high-resolution Doppler analysis
of multipath over-the-horizon radar (OTHR) signals. This is an effective technique
that enables improved target parameter estimation in OTHR operations. However,
due to high proximity of these Doppler signatures in TF domain, their separation
poses a challenging problem. By utilizing signal self-stationarization and ensuring IF
continuity, the developed approaches show excellent performance to handle multiple
signal components with variations in their amplitude levels.
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