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.

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.

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.

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.

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.

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.

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.

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The radar transmitter identification problem involves the identification of a specific radar transmitter based on a received pulse. The radar transmitters are of identical make and model. This makes the problem challenging since the differences between radars of identical make and model will be solely due to component tolerances and variation. Radar pulses also vary in time and frequency which means that the problem is non-stationary. Because of this fact, time-frequency representations such as shift-invariant quadratic time-frequency representations (Cohen’s class) and wavelets were used. A model for a radar transmitter was developed. This consisted of an analytical solution to a pulse-forming network and a linear model of an oscillator. Three signal classification algorithms were developed. A signal classifier was developed that used a radially Gaussian Cohen’s class transform. This time-frequency representation was refined to increase the classification accuracy. The classification was performed with a support vector machine classifier. The second signal classifier used a wavelet packet transform to calculate the feature values. The classification was performed using a support vector machine. The third signal classifier also used the wavelet packet transform to calculate the feature values but used a Universum type classifier for classification. This classifier uses signals from the same domain to increase the classification accuracy. The classifiers were compared against each other on a cubic and exponential chirp test problem and the radar transmitter model. The classifier based on the Cohen’s class transform achieved the best classification accuracy. The classifier based on the wavelet packet transform achieved excellent results on an Electroencephalography (EEG) test dataset. The complexity of the wavelet packet classifier is significantly lower than the Cohen’s class classifier. Copyright / Dissertation (MEng)--University of Pretoria, 2010. / Electrical, Electronic and Computer Engineering / unrestricted

La presente tesis cuenta con dos objetivos. Por una parte introducir y validar un método de análisis de corrientes estatóricas para el diagnóstico de máquinas de inducción conectadas a la red que operan en estado transitorio, basado en el uso de filtros de rechazo de frecuencia en combinación con la distribución de Wigner-Ville, con especial interés en su aplicación para la detección incipiente de defectos. El segundo objetivo consiste en replicar de la manera más fidedigna posible el proceso de rotura de una barra en el rótor de un motor de inducción. Para ello se ha diseñado un ensayo encaminado a provocar dicha avería sometiendo un motor a fatiga. Con este objetivo se ha construido un banco de pruebas y emplazado los sensores necesarios, así como un sistema de recogida de datos de manera automatizada. Adicionalmente, se ha diseñado los programas de procesamiento de los mismos, también para ser llevado a cabo de la manera lo más desatendida posible. / Climente Alarcón, V. (2012). Aportación al mantenimiento predictivo de motores de inducción mediante modernas técnicas de análisis de la señal [Tesis doctoral]. Universitat Politècnica de València. https://doi.org/10.4995/Thesis/10251/15915