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Adaptive filtering techniques are used in a wide range of applications, including echo cancellation, adaptive equalization, adaptive noise cancellation, and adaptive beamforming. The performance of an adaptive filtering algorithm is evaluated based on its convergence rate, misadjustment, computational requirements, and numerical robustness. We attempt to improve the performance by developing new adaptation algorithms and by using "unconventional" structures for adaptive filters. Part I of this dissertation presents a new adaptation algorithm, which we have termed the Normalized LMS algorithm with Orthogonal Correction Factors (NLMS-OCF). The NLMS-OCF algorithm updates the adaptive filter coefficients (weights) on the basis of multiple input signal vectors, while NLMS updates the weights on the basis of a single input vector. The well-known Affine Projection Algorithm (APA) is a special case of our NLMS-OCF algorithm. We derive convergence and tracking properties of NLMS-OCF using a simple model for the input vector. Our analysis shows that the convergence rate of NLMS-OCF (and also APA) is exponential and that it improves with an increase in the number of input signal vectors used for adaptation. While we show that, in theory, the misadjustment of the APA class is independent of the number of vectors used for adaptation, simulation results show a weak dependence. For white input the mean squared error drops by 20 dB in about 5N/(M+1) iterations, where N is the number of taps in the adaptive filter and (M+1) is the number of vectors used for adaptation. The dependence of the steady-state error and of the tracking properties on the three user-selectable parameters, namely step size, number of vectors used for adaptation (M+1), and input vector delay D used for adaptation, is discussed. While the lag error depends on all of the above parameters, the fluctuation error depends only on step size. Increasing D results in a linear increase in the lag error and hence the total steady-state mean-squared error. The optimum choices for step size and M are derived. Simulation results are provided to corroborate our analytical results. We also derive a fast version of our NLMS-OCF algorithm that has a complexity of O(NM). The fast version of the algorithm performs orthogonalization using a forward-backward prediction lattice. We demonstrate the advantages of using NLMS-OCF in a practical application, namely stereophonic acoustic echo cancellation. We find that NLMS-OCF can provide faster convergence, as well as better echo rejection, than the widely used APA. While the first part of this dissertation attempts to improve adaptive filter performance by refining the adaptation algorithm, the second part of this work looks at improving the convergence rate by using different structures. From an abstract viewpoint, the parameterization we decide to use has no special significance, other than serving as a vehicle to arrive at a good input-output description of the system. However, from a practical viewpoint, the parameterization decides how easy it is to numerically minimize the cost function that the adaptive filter is attempting to minimize. A balanced realization is known to minimize the parameter sensitivity as well as the condition number for Grammians. Furthermore, a balanced realization is useful in model order reduction. These properties of the balanced realization make it an attractive candidate as a structure for adaptive filtering. We propose an adaptive filtering algorithm based on balanced realizations. The third part of this dissertation proposes a unit-norm-constrained equation-error based adaptive IIR filtering algorithm. Minimizing the equation error subject to the unit-norm constraint yields an unbiased estimate for the parameters of a system, if the measurement noise is white. The proposed algorithm uses the hyper-spherical transformation to convert this constrained optimization problem into an unconstrained optimization problem. It is shown that the hyper-spherical transformation does not introduce any new minima in the equation error surface. Hence, simple gradient-based algorithms converge to the global minimum. Simulation results indicate that the proposed algorithm provides an unbiased estimate of the system parameters. / Ph. D.

There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality.<p> In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated.<p> In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance.

There is a growing demand for the high quality TV programs such as High Definition TV (HDTV). The CATV network is often a suitable solution to address this demand using a CATV modem delivering high data rate digital signals in a cost effective manner, thereby, utilizing a complex digital modulation scheme is inevitable. Exploiting complex modulation schemes, entails a more sophisticated modulator and distribution system with much tighter tolerances. However, there are always distortions introduced to the modulated signal in the modulator degrading signal quality.<p> In this research, the effect of distortions introduced by the RF band pass filter in the modulator will be considered which cause degradations on the quality of the output Quadrature Amplitude Modulated (QAM) signal. Since the RF filter's amplitude/group delay distortions are not symmetrical in the frequency domain, once translated into the base band they have a complex effect on the QAM signal. Using Matlab, the degradation effects of these distortions on the QAM signal such as Bit Error Rate (BER) is investigated.<p> In order to compensate for the effects of the RF filter distortions, two different methods are proposed. In the first method, a complex base band compensation filter is placed after the pulse shaping filter (SRRC). The coefficients of this complex filter are determined using an optimization algorithm developed during this research. The second approach, uses a pre-equalizer in the form of a Feed Forward FIR structure placed before the pulse shaping filter (SRRC). The coefficients of this pre-equalizer are determined using the equalization algorithm employed in a test receiver, with its tap weights generating the inverse response of the RF filter. The compensation of RF filter distortions in base band, in turn, improves the QAM signal parameters such as Modulation Error Ratio (MER). Finally, the MER of the modulated QAM signal before and after the base band compensation is compared between the two methods, showing a significant enhancement in the RF modulator performance.

The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.

The design of nearly linear-phase recursive digital filters using constrained optimization is investigated. The design technique proposed is expected to be useful in applications where both magnitude and phase response specifications need to be satisfied. The overall constrained optimization method is formulated as a quadratic programming problem based on Newton’s method. The objective function, its gradient vector and Hessian matrix as well as a set of linear constraints are derived. In this analysis, the independent variables are assumed to be the transfer function coefficients. The filter stability issue and convergence efficiency, as well as a ‘real axis attraction’ problem are solved by integrating the corresponding bounds into the linear constraints of the optimization method. Also, two initialization techniques for providing efficient starting points for the optimization are investigated and the relation between the zero and pole positions and the group delay are examined. Based on these ideas, a new objective function is formulated in terms of the zeros and poles of the transfer function expressed in polar form and integrated into the optimization process. The coefficient-based and polar-based objective functions are tested and compared and it is shown that designs using the polar-based objective function produce improved results. Finally, several other modern methods for the design of nearly linear-phase recursive filters are compared with the proposed method. These include an elliptic design combined with an optimal equalization technique that uses a prescribed group delay, an optimal design method with robust stability using conic-quadratic-programming updates, and an unconstrained optimization technique that uses parameterization to guarantee filter stability. It was found that the proposed method generates similar or improved results in all comparative examples suggesting that the new method is an attractive alternative for linear-phase recursive filters of orders up to about 30.

This thesis presents the Deriche edge detector as an interesting alternative to the commonly used edge detectors. The Deriche edge detector's design is presented to the reader as well as its strengths and weaknesses. Performance issues of the Deriche edge detector are described in comparison with the Canny edge detector together with recommendations for using the Deriche detector. Finally, edge detection quality of the Deriche edge detector is compared to the Canny edge detector using robust subjective evaluation method.

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La thèse porte sur l'impact d'optimisations algorithmiques pour la synthèse automatique HLS pour ASIC. Ces optimisations algorithmiques sont des transformations de haut niveau, qui de part leur nature intrinsèque restent hors de porter des compilateurs modernes, même les plus optimisants. Le but est d'analyser l'impact des optimisations et transformations de haut niveau sur la surface, la consommation énergétique et la vitesse du circuit ASIC. Les trois algorithmes évalués sont les filtres non récursifs, les filtres récursifs et un algorithme de détection de mouvement. Sur chaque exemple, des gains ont été possibles en vitesse et/ou en surface et/ou en consommation. Le gain le plus spectaculaire est un facteur x12.6 de réduction de l'énergie tout en maitrisant la surface de synthèse et en respectant la contrainte d'exécution temps réel. Afin de mettre en perspective les résultats (consommation et vitesse), un benchmark supplémentaire a été réalisé sur un microprocesseur ST XP70 avec extension VECx, un processeur ARM Cortex avec extension Neon et un processeur Intel Penryn avec extensions SSE. / The thesis deals with the impact of algorithmic transforms for HLS synthesis for ASIC. These algorithmic transforms are high level transforms that are beyond the capabilities of modern optimizing compilers. The goal is to analyse the impact of the High level transforms on area execution time and energy consumption. Three algorithms have been analyzed: non recursive filters, recursive filter and a motion detection application. On each algorithm, the optimizations and transformations lead to speedups and area/surface gains. The most impressive gain in energy reduction is a factor x12.6, while the area remains constant and the execution time smaller than the real-time constraint. A benchmark has been done on SIMD general purpose processor to compare the impact of the high level transforms: ST XP70 microprocessor with VECx extension, ARM Cortex with Non extension and Intel Penryn with SSE extension.

This thesis introduces the reader into RespiHeart, which is a product under development. RespiHeart is an complement/alternative to the regular Pulse Oximeter and is intended to be used within the health care sector for combined measurements and communication on open inexpensive platforms. This thesis evaluates interaction between RespiHeart and a Raspberry Pi 3 Model B to evaluate if the computer is capable of handling the data from RespiHeart and make signal processing. Python is used throughout the whole project and is a suitable language for interaction and signal processing in real time. / Detta examensarbete introducerar läsaren till RespiHeart, en ny trådlös produkt som är under utveckling. RespiHeart är ett komplement/alternativ till den nuvarande Pulsoximetern och är tänkt att användas inom sjukvården för analys, kommuniakation och kombinerade mätningar på öppna billiga plattformar. Detta project utvärderar interaktionen mellan RespiHeart och en Raspberry Pi 3 Model B för att undersöka om datorn är kapabel till att hantera datan från RespiHeart samt göra signal processing i real tid. Programmeringsspråket Python användes under hela projektet och är ett lämpligt språk att använda för interation och signal processing i real tid.