A proper time-frequency transform technique suppresses the blurring and smearing effect of the time-varying Doppler shift on the target image. The conventional target imaging method uses the Fourier transform for extracting the Doppler shift from the received radar pulse. Since the Doppler shift is timevarying for rotating targets, the constructed images will be degraded. In this thesis, the Doppler shift information required for the Range-Doppler image of the target is extracted by using high resolution time-frequency transform techniques. The Wigner-Ville Distribution and the Adaptive Gabor Representation with the Coarse-to-Fine and the Matching Pursuit Search Algorithms are examined techniques for the target imaging system. The modified Matching Pursuit Algorithm, the Matching Pursuit with Reduced Dictionary is proposed which decreases the signal processing time required by the Adaptive Gabor Representation. The Hybrid Matching Pursuit Search Algorithm is also introduced in this thesis work and the Coarse-to-Fine Algorithm and the Matching Pursuit Algorithm are combined for obtaining better representation quality of a signal in the time-frequency domain. The stated techniques are applied on to the sample signals and compared with each other. The application of these techniques in the target imaging system is also performed for the simulated aircrafts.

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.

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.