The doctoral thesis focuses on signal representation in the time-frequency domain with constant resolution. In theoretical introduction the possibilities of displaying a signal in time and frequency are summarized. Attention is concentrated on comparison of short-time Fourier Transform (STFT) and Wigner-Ville Distribution (WVD). The latter achieves a significantly better resolution, especially for a linearly modulated signal. The disadvantage of WVD, which is the presence of interferences resulting from the calculation of the instantaneous autocorrelation function, is described in detail. These interferences are due to the presence of multiple components in the signal or its non-linear modulation. Subsequently, several methods are discussed, which can suppress these interferences, but at the cost of resolution loss. One of the interference suppression methods is smoothed pseudo Wigner-Ville distribution. It is further used in this thesis for the analysis of interference suppression when various filtrations in the time-frequency plane are applied. Several signals with multiple components or various non-linear modulations are used. Based on the analysis, a method using a set of variously smoothed pseudo Wigner-Ville distributions is designed to estimate the time-frequency representation with high resolution and minimal interferences. To compare the results to other methods, the quantitative metrics used in the literature are compared. To select the appropriate one a new metric is suggested. It is applicable to simulated signals and uses mean square error. Based on the comparison, the Stankovi\' measure is selected as the most appropriate for comparing results. The selected metric is used to determine the appropriate minimal number of differently smoothed pseudo Wigner-Ville distributions. Using the selected metric, the proposed method is compared with other methods. These are STFT with optimized window length, S-method with optimized parameter and optimization method using radial Gaussian kernel (RGK). These methods are compared based on the set of signals previously used for interference suppression analysis. In addition, noises are added to the signals. Finally, the methods are also compared based on the real bat echo signal. In conclusion, the proposed method outperforms the compared methods in suppressing interference and resolution.

In this thesis work, time-frequency filtering of nonstationary signals in noise using Wigner-Ville Distribution is investigated. Continuous-time, discrete-time and discrete Wigner Ville Distribution definitions, their relations, and properties are given. Time-Frequency Peak Filtering Method is presented. The effects of different parameters on the performance of the method are investigated, and the results are presented. Time-Varying Wiener Filter is presented. Using simulations it is shown that the performance of the filter is good at SNR levels down to -5 dB. It is proposed and shown that the performance of the filter improves by using Support Vector Machines. The presented time-frequency filtering techniques are applied on test signals and on a real world signal. The results obtained by the two methods and also by classical zero-phase low-pass filtering are compared. It is observed that for low sampling rates Time-Varying Wiener Filter, and for high sampling rates Time-Frequency Peak Filter performs better.

Multiple Signal Classification (MUSIC) Algorithm based and Wigner Distribution-Principal Component Analysis (WD-PCA) based classification techniques are very recently suggested resonance region approaches for electromagnetic target classification. In this thesis, performances of these two techniques will be compared concerning their robustness for noise and their capacity to handle large number of candidate targets. In this context, classifier design simulations will be demonstrated for target libraries containing conducting and dielectric spheres and for dielectric coated conducting spheres. Small scale aircraft targets modeled by thin conducting wires will also be used in classifier design demonstrations.

The Self-Organizing Map (SOM) is a type of neural network that forms a regular grid of neurons where clusters of neurons represent different classes of targets. The aim of this thesis is to design electromagnetic target classifiers by using the Self-Organizing Map (SOM) type artificial neural networks for dielectric and conducting objects with simple or complex geometries. Design simulations will be realized for perfect dielectric spheres and also for small-scaled aircraft targets modeled by thin conducting wires. The SOM classifiers will be designed by target features extracted from the scattered signals of targets at various aspects by using the Wigner distribution. Noise performance of classifiers will be improved by using slightly noisy input data in SOM training.

This thesis applies an electromagnetic feature extraction technique to design electromagnetic target classifiers for conductors, dielectrics and dielectric coated conductors using their natural resonance related late-time scattered responses. Classifier databases contain scattered data at only a few aspects for each candidate target. The targets are dielectric spheres of varying sizes and refractive indices, perfectly conducting spheres varying sizes and dielectric coated conducting spheres of varying refractive indices and thickness in coating. The applied classifier design technique is suitable for real-time target classification because of the computational efficiency of feature extraction and decision making approaches. The Wigner-Ville Distribution (WD) is employed in this study in addition to the Principal Components Analysis (PCA) technique to extract target features mainly from late-time target responses. WD is applied to the back-scattered responses at different aspects. To decrease aspect dependency, feature vectors are extracted from selected late-time portions of the WD outputs that include natural resonance related information. Principal components analysis is also used to fuse the feature vectors and/or late-time target responses extracted from reference aspects of a given target into a single characteristic feature vector for each target to further reduce aspect dependency.

Most signal processing methods were developed for continuous signals. Digital devices, such as the computer, process only discrete signals. This dissertation proposes new techniques to accurately define and efficiently implement an important signal processing method---the time--frequency distribution (TFD)---using discrete signals. The TFD represents a signal in the joint time--frequency domain. Because these distributions are a function of both time and frequency they, unlike traditional signal processing methods, can display frequency content that changes over time. TFDs have been used successfully in many signal processing applications as almost all real-world signals have time-varying frequency content. Although TFDs are well defined for continuous signals, defining and computing a TFD for discrete signals is problematic. This work overcomes these problems by making contributions to the definition, computation, and application of discrete TFDs. The first contribution is a new discrete definition of TFDs. A discrete TFD (DTFD) should be free from the sampling-related distortion known as aliasing and satisfy all the important mathematical properties that the continuous TFD satisfies. Many different DTFD definitions exist but none come close to attaining this ideal. I propose three new components which make up the DTFD: 1) a new discrete Wigner--Ville distribution (DWVD) definition which satisfies all properties, 2) a new discrete analytic signal which minimises aliasing in the DWVD, and 3) a new method to define and convolve the discrete kernel with the DWVD to produce the DTFD. The result: a DTFD definition that, relative to the existing definitions, better approximates the ideal DTFD. The second contribution is two sets of computationally efficient algorithms to compute the proposed DTFD. The first set of algorithms computes the DTFD exactly; the second set requires less memory than the first set by computing time- and, or frequency-decimated versions of the DTFD. Both sets of algorithms reduce the computational load by exploiting symmetries in the DTFD and by constructing kernel-specific algorithms for four different kernel types. The third, and final, contribution is a biomedical application for the proposed DTFD and algorithms. This application is to accurately detect seizure events in newborn electroencephalogram (EEG) signals. Existing detection methods do not perform well enough for use in a clinical setting. I propose a new method which is more robust than existing methods and show how using the proposed DTFD, comparative to an existing DTFD, improves detection performance for this method. In summary, this dissertation makes practical contributions to the area of time--frequency signal processing by proposing an improved DTFD definition, efficient DTFD algorithms, and an improved newborn EEG seizure detection method using DTFDs.

Brushless Direct Current (BLDC) motors are one of the motor types rapidly gaining popularity. BLDC motors are being increasingly used in critical high performance industries such as appliances, automotive, aerospace, consumer, medical, industrial automation equipment and instrumentation. Fault detection and condition monitoring of BLDC machines is therefore assuming a new importance. The objective of this research is to advance the field of rotor and load fault diagnosis in BLDC machines operating in a variety of operating conditions ranging from constant speed to continuous transient operation. This objective is addressed as three parts in this research. The first part experimentally characterizes the effects of rotor faults in the stator current and voltage of the BLDC motor. This helps in better understanding the behavior of rotor defects in BLDC motors. The second part develops methods to detect faults in loads coupled to BLDC motors by monitoring the stator current. As most BLDC applications involve non-stationary operating conditions, the diagnosis of rotor faults in non-stationary conditions forms the third and most important part of this research. Several signal processing techniques are reviewed to analyze non-stationary signals. Three new algorithms are proposed that can track and detect rotor faults in non-stationary or transient current signals.

Inverse Synthetic Aperture Radar coherently processes the return signal from the target in order to construct the image of the target. The conventional methodology used for obtaining the image is the Fourier transform which is not capable of suppressing the Doppler change in the return signal. As a result, Range-Doppler image is degraded. A proper time-frequency transform suppresses the degradation due to time varying Doppler shift. In this thesis, high resolution joint-time frequency transformations that can be used in place of the conventional method are evaluated. Wigner-Ville Distribution, Adaptive Gabor Representation with Coarse-to-Fine search algorithm, and Time-Frequency Distribution Series are examined for the target imaging system. The techniques applied to sample signals compared with each other. The computational and memorial complexity of the methods are evaluated and compared to each other and possible improvements are discussed. The application of these techniques in the target imaging system is also performed and resulting images compared to each other.

Brain Computer Interfaces (BCIs) are systems developed in order to control devices by using only brain signals. In BCI systems, different mental activities to be performed by the users are associated with different actions on the device to be controlled. Spelling Paradigm is a BCI application which aims to construct the words by finding letters using P300 signals recorded via channel electrodes attached to the diverse points of the scalp. Reducing the letter detection error rates and increasing the speed of letter detection are crucial for Spelling Paradigm. By this way, disabled people can express their needs more easily using this application. In this thesis, two different methods, Support Vector Machine (SVM) and AdaBoost, are used for classification in the analysis. Classification and Regression Trees is used as the weak classifier of the AdaBoost. Time-frequency domain characteristics of P300 evoked potentials are analyzed in addition to time domain characteristics. Wigner-Ville Distribution is used for transforming time domain signals into time-frequency domain. It is observed that classification results are better in time domain. Furthermore, optimum subset of channels that models P300 signals with minimum error rate is searched. A method that uses both SVM and AdaBoost is proposed to select channels. 12 channels are selected in time domain with this method. Also, effect of dimension reduction is analyzed using Principal Component Analysis (PCA) and AdaBoost methods.

The problem studied in this thesis, is the classification of the small-scale aircraft targets by using a natural resonance based electromagnetic feature extraction technique. The aircraft targets are modeled by perfectly conducting, thin wire structures. The electromagnetic back-scattered data used in the classification process, are numerically generated for five aircraft models. A contemporary signal processing tool, the Wigner-Ville distribution is employed in this study in addition to using the principal components analysis technique to extract target features mainly from late-time target responses. The Wigner-Ville distribution (WD) is applied to the electromagnetic back-scattered responses from different aspects. Then, feature vectors are extracted from suitably chosen late-time portions of the WD outputs, which include natural resonance related v information, for every target and aspect to decrease aspect dependency. The database of the classifier is constructed by the feature vectors extracted at only a few reference aspects. Principal components analysis is also used to fuse the feature vectors and/or late-time aircraft responses extracted from reference aspects of a given target into a single characteristic feature vector of that target to further reduce aspect dependency. Consequently, an almost aspect independent classifier is designed for small-scale aircraft targets reaching high correct classification rate.