Performance analysis of adaptive lattice filters for FM signals and alpha-stable processes

The performance of an adaptive filter may be studied through the behaviour of the optimal and adaptive coefficients in a given environment. This thesis investigates the performance of finite impulse response adaptive lattice filters for two classes of input signals: (a) frequency modulated signals with polynomial phases of order p in complex Gaussian white noise (as nonstationary signals), and (b) the impulsive autoregressive processes with alpha-stable distributions (as non-Gaussian signals). Initially, an overview is given for linear prediction and adaptive filtering. The convergence and tracking properties of the stochastic gradient algorithms are discussed for stationary and nonstationary input signals. It is explained that the stochastic gradient lattice algorithm has many advantages over the least-mean square algorithm. Some of these advantages are having a modular structure, easy-guaranteed stability, less sensitivity to the eigenvalue spread of the input autocorrelation matrix, and easy quantization of filter coefficients (normally called reflection coefficients). We then characterize the performance of the stochastic gradient lattice algorithm for the frequency modulated signals through the optimal and adaptive lattice reflection coefficients. This is a difficult task due to the nonlinear dependence of the adaptive reflection coefficients on the preceding stages and the input signal. To ease the derivations, we assume that reflection coefficients of each stage are independent of the inputs to that stage. Then the optimal lattice filter is derived for the frequency modulated signals. This is performed by computing the optimal values of residual errors, reflection coefficients, and recovery errors. Next, we show the tracking behaviour of adaptive reflection coefficients for frequency modulated signals. This is carried out by computing the tracking model of these coefficients for the stochastic gradient lattice algorithm in average. The second-order convergence of the adaptive coefficients is investigated by modeling the theoretical asymptotic variance of the gradient noise at each stage. The accuracy of the analytical results is verified by computer simulations. Using the previous analytical results, we show a new property, the polynomial order reducing property of adaptive lattice filters. This property may be used to reduce the order of the polynomial phase of input frequency modulated signals. Considering two examples, we show how this property may be used in processing frequency modulated signals. In the first example, a detection procedure in carried out on a frequency modulated signal with a second-order polynomial phase in complex Gaussian white noise. We showed that using this technique a better probability of detection is obtained for the reduced-order phase signals compared to that of the traditional energy detector. Also, it is empirically shown that the distribution of the gradient noise in the first adaptive reflection coefficients approximates the Gaussian law. In the second example, the instantaneous frequency of the same observed signal is estimated. We show that by using this technique a lower mean square error is achieved for the estimated frequencies at high signal-to-noise ratios in comparison to that of the adaptive line enhancer. The performance of adaptive lattice filters is then investigated for the second type of input signals, i.e., impulsive autoregressive processes with alpha-stable distributions . The concept of alpha-stable distributions is first introduced. We discuss that the stochastic gradient algorithm which performs desirable results for finite variance input signals (like frequency modulated signals in noise) does not perform a fast convergence for infinite variance stable processes (due to using the minimum mean-square error criterion). To deal with such problems, the concept of minimum dispersion criterion, fractional lower order moments, and recently-developed algorithms for stable processes are introduced. We then study the possibility of using the lattice structure for impulsive stable processes. Accordingly, two new algorithms including the least-mean P-norm lattice algorithm and its normalized version are proposed for lattice filters based on the fractional lower order moments. Simulation results show that using the proposed algorithms, faster convergence speeds are achieved for parameters estimation of autoregressive stable processes with low to moderate degrees of impulsiveness in comparison to many other algorithms. Also, we discuss the effect of impulsiveness of stable processes on generating some misalignment between the estimated parameters and the true values. Due to the infinite variance of stable processes, the performance of the proposed algorithms is only investigated using extensive computer simulations.

The development of science concepts emergent from science museum and post-visit activity experiences : students' construction of knowledge

This research investigated students' construction of knowledge about the topics of magnetism and electricity emergent from a visit to an interactive science centre and subsequent classroom-based activities linked to the science centre exhibits. The significance of this study is that it analyses critically an aspect of school visits to informal learning centres that has been neglected by researchers in the past, namely the influence of post-visit activities in the classroom on subsequent learning and knowledge construction. Employing an interpretive methodology, the study focused on three areas of endeavour. Firstly, the establishment of a set of principles for the development of post-visit activities, from a constructivist framework, to facilitate students' learning of science. Secondly, to describe and interpret students' scientific understandings : prior t o a visit t o a science museum; following a visit t o a science museum; and following post-visit activities that were related to their museum experiences. Finally, to describe and interpret the ways in which students constructed their understandings: prior to a visit to a science museum; following a visit to a science museum; and following post-visit activities directly related to their museum experiences. The study was designed and implemented in three stages: 1) identification and establishment of the principles for design and evaluation of post-visit activities; 2) a pilot study of specific post-visit activities and data gathering strategies related to student construction of knowledge; and 3) interpretation of students' construction of knowledge from a visit to a science museum and subsequent completion of post-visit activities, which constituted the main study. Twelve students were selected from a year 7 class to participate in the study. This study provides evidence that the series of post-visit activities, related to the museum experiences, resulted in students constructing and reconstructing their personal knowledge of science concepts and principles represented in the science museum exhibits, sometimes towards the accepted scientific understanding and sometimes in different and surprising ways. Findings demonstrate the interrelationships between learning that occurs at school, at home and in informal learning settings. The study also underscores for teachers and staff of science museums and similar centres the importance of planning pre- and post-visit activities, not only to support the development of scientific conceptions, but also to detect and respond to alternative conceptions that may be produced or strengthened during a visit to an informal learning centre. Consistent with contemporary views of constructivism, the study strongly supports the views that : 1) knowledge is uniquely structured by the individual; 2) the processes of knowledge construction are gradual, incremental, and assimilative in nature; 3) changes in conceptual understanding are can be interpreted in the light of prior knowledge and understanding; and 4) knowledge and understanding develop idiosyncratically, progressing and sometimes appearing to regress when compared with contemporary science. This study has implications for teachers, students, museum educators, and the science education community given the lack of research into the processes of knowledge construction in informal contexts and the roles that post-visit activities play in the overall process of learning.