Novel Digital Alias-Free Signal Processing Approaches to FIR Filtering Estimation

This thesis aims at developing a new methodology of filtering continuous-time bandlimited signals and piecewise-continuous signals from their discrete-time samples. Unlike the existing state-of-the-art filters, my filters are not adversely affected by aliasing, allowing the designers to flexibly select the sampling rates of the processed signal to reach the required accuracy of signal filtering rather than meeting stiff and often demanding constraints imposed by the classical theory of digital signal processing (DSP). The impact of this thesis is cost reduction of alias-free sampling, filtering and other digital processing blocks, particularly when the processed signals have sparse and unknown spectral support. Novel approaches are proposed which can mitigate the negative effects of aliasing, thanks to the use of nonuniform random/pseudorandom sampling and processing algorithms. As such, the proposed approaches belong to the family of digital alias-free signal processing (DASP). Namely, three main approaches are considered: total random (ToRa), stratified (StSa) and antithetical stratified (AnSt) random sampling techniques. First, I introduce a finite impulse response (FIR) filter estimator for each of the three considered techniques. In addition, a generalised estimator that encompasses the three filter estimators is also proposed. Then, statistical properties of all estimators are investigated to assess their quality. Properties such as expected value, bias, variance, convergence rate, and consistency are all inspected and unveiled. Moreover, closed-form mathematical expression is devised for the variance of each single estimator. Furthermore, quality assessment of the proposed estimators is examined in two main cases related to the smoothness status of the filter convolution’s integrand function, \u1d454(\u1d461,\u1d70f)∶=\u1d465(\u1d70f)ℎ(\u1d461−\u1d70f), and its first two derivatives. The first main case is continuous and differentiable functions \u1d454(\u1d461,\u1d70f), \u1d454′(\u1d461,\u1d70f), and \u1d454′′(\u1d461,\u1d70f). Whereas in the second main case, I cover all possible instances where some/all of such functions are piecewise-continuous and involving a finite number of bounded discontinuities. Primarily obtained results prove that all considered filter estimators are unbiassed and consistent. Hence, variances of the estimators converge to zero after certain number of sample points. However, the convergence rate depends on the selected estimator and which case of smoothness is being considered. In the first case (i.e. continuous \u1d454(\u1d461,\u1d70f) and its derivatives), ToRa, StSa and AnSt filter estimators converge uniformly at rates of \u1d441−1, \u1d441−3, and \u1d441−5 respectively, where 2\u1d441 is the total number of sample points. More interestingly, in the second main case, the convergence rates of StSa and AnSt estimators are maintained even if there are some discontinuities in the first-order derivative (FOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for StSa estimator) or in the second-order derivative (SOD) with respect to \u1d70f of \u1d454(\u1d461,\u1d70f) (for AnSt). Whereas these rates drop to \u1d441−2 and \u1d441−4 (for StSa and AnSt, respectively) if the zero-order derivative (ZOD) (for StSa) and FOD (for AnSt) are piecewise-continuous. Finally, if the ZOD of \u1d454(\u1d461,\u1d70f) is piecewise-continuous, then the uniform convergence rate of the AnSt estimator further drops to \u1d441−2. For practical reasons, I also introduce the utilisation of the three estimators in a special situation where the input signal is pseudorandomly sampled from otherwise uniform and dense grid. An FIR filter model with an oversampled finite-duration impulse response, timely aligned with the grid, is proposed and meant to be stored in a lookup table of the implemented filter’s memory to save processing time. Then, a synchronised convolution sum operation is conducted to estimate the filter output. Finally, a new unequally spaced Lagrange interpolation-based rule is proposed. The so-called composite 3-nonuniform-sample (C3NS) rule is employed to estimate area under the curve (AUC) of an integrand function rather than the simple Rectangular rule. I then carry out comparisons for the convergence rates of different estimators based on the two interpolation rules. The proposed C3NS estimator outperforms other Rectangular rule estimators on the expense of higher computational complexity. Of course, this extra cost could only be justifiable for some specific applications where more accurate estimation is required

FIR Filtering of Discontinuous Signals: A Random-Stratified Sampling Approach

This paper presents a novel approach, based on random stratified sampling (StSa) technique, to estimate the output of a finite impulse response (FIR) filter when the input signal is either a piecewise-continuous function having first-derivative discontinuities (FDDs), or a piecewise-discontinuous function, i.e. having zero-derivative discontinuities (ZDDs). The proposed approach investigates the implications of such discontinuities on the output signal and its statistical properties. Mainly, we devise mathematical expressions for the variance of the StSa estimator in the two cases above, along with other minor special cases. It is found that the uniform convergence rate of the estimator, in the FDDs case, is N^{-3}, where N is the number of random samples. However, the variance in the ZDDs case is adversely affected by the existence of discontinuities. We prove that it converges more slowly with a uniform rate of N^{-2}

DASP Implementation of Continuous-Time, Finite-Impulse-Response Systems

Digital Alias-free Signal Processing (DASP) uses random sampling to mitigate aliasing. This paper investigates the use of DASP for realization of continuous-time, linear, time-invariant systems with finite-duration impulse response. We propose a random sampling scheme and suitable processing algorithm to produce an estimator of the target output. The estimator is unbiased, and its variance is guaranteed to converge to zero at least at O(T) rate, where T is the average distance between consecutive sampling instants. If the input signal and system impulse response are piecewise continuous and satisfy some benign conditions, the convergence rate is at least O(T^2). But if they are continuous everywhere, the rate increases to O(T^3)

Comparison Between Uniform and Nonuniform Interpolation Techniques for Digital Alias-free FIR Filtering

In this paper, we propose three grid-based nonuniform interpolation techniques to find the AUC of the convolution operation of a digital alias-free FIR filter. Up to the authors’ knowledge, these techniques were not addressed in literature before. We call them composite 3-nonuniform-sample (C3NS), composite 4-nonuniform-sample (C4NS) and composite 5-nonuniform-sample (C5NS) rules. They are named after the traditional composite Simpson’s 1/3 rule which is usually used in second-order polynomial interpolation of equally-spaced sampling points. The proposed new rules shows better estimated results than the uniform-based ones when the number of sampling points doesn’t match the required Nyquist rate. Moreover, we prove that composite Simpson’s 1/3 rule is more accurate than composite Simpson’s 3/8 rule mathematically and by simulation

Antithetical Stratified Sampling Estimator for Filtering Signals with Discontinuities

A novel approach to signal filtering using digital alias-free signal processing (DASP) is presented in this paper. We propose an unbiased, fast-converging estimator of the output of a finite impulse response (FIR) continuous-time filter. The estimator processes 2N signal samples collected with the use of random antithetical stratified (AnSt) sampling technique. To assess the estimator convergence rate as the function of N, we consider various forms of smoothness of the input signal, filter impulse response and windowing function. The cases are piecewise-continuous second-order derivative (SOD), piecewise-continuous first-order derivative (FOD) and piecewise-continuous zero-order derivative (ZOD). In each case we assume that the respective derivative has a finite number of bounded discontinuities. We prove that the proposed estimator converges to the true filter output at the rate of N^(-5) in the first case. But for the other two the rate drops to N^(-4) and N^(-2) respectively

Leading with Love and Its Relationship to Faculty Members Job Loyalty in Jordanian Universities

In This study we investigate the relationship between academic leaders practice of leading with love and faculty members job loyalty in Jordanian public universities, the study recruited (358) faculty members. The study finds that academic leaders practice leading with love to a high degree and that faculty members have high job loyalty. Additionally, there is a statistically significant positive relationship between practicing leadership by love and faculty members job loyalty. The study suggests that adopting leadership by love can enhance employee performance and achieve job satisfaction in universities

Interpersonal Communication Model for Children with Special Needs

The emphasis of this study is on how children who have special needs communicate with one another (deaf). Participant observation, interviews, and documentation are among the methods that are used throughout the data-gathering process. According to the findings of the research, the interpersonal communication model for deaf children is made up of two different models, one of which is the dyadic communication model. This kind of dyadic communication does not take place during the teaching and learning process; rather, it takes place outside of regular class hours. The whole communication model comes in at number two. Throughout the teaching and learning process, as well as outside of regular class hours, total communication is used. employing both symbolic interaction theory and ethnography theory as analytic frameworks. This demonstrates that the process of the interpersonal communication model is carried out face to face and at close distances, which makes it simpler to speak with deaf children since they are more accessible

The weight-loss experience : qualitative exploration

BACKGROUND: Long-term weight management consists of weight-loss, weight-loss maintenance, and weight-gain stages. Qualitative insights into weight management are now appearing in the literature however research appears to be biased towards explorations of weight-loss maintenance. The qualitative understanding of weight loss, which begets weight-loss maintenance and might establish the experiences and behaviours necessary for successful long-term weight management, is comparatively under-investigated. The aim of this study was to investigate the weight-loss experiences of a sample of participants not aligned to clinical intervention research, in order to understand the weight-loss experiences of a naturalistic sample. METHODS: Participants (n=8) with weight-loss (n=4) and weight-maintenance experiences (n=4) were interviewed using a semi-structured interview to understand the weight-loss experience. Interview data was analysed thematically using Framework Analysis and was underpinned by realist meta-theory. RESULTS: Weight loss was experienced as an enduring challenge, where factors that assisted weight loss were developed and experienced dichotomously to factors that hindered it. Participants described barriers to (dichotomous thinking, environments, social pressures and weight centeredness) and facilitators of (mindfulness, knowledge, exercise, readiness to change, structure, self-monitoring and social support) their weight-loss goals in rich detail, highlighting that weight loss was a complex experience. CONCLUSIONS: Weight loss was a difficult task, with physical, social, behavioural and environmental that appeared to assist and inhibit weight-loss efforts concurrently. Health professionals might need to better understand the day-to-day challenges of dieters in order to provide more effective, tailored treatments. Future research should look to investigate the psycho-social consequences of weight-loss dieting, in particular self-imposed social exclusion and spousal sabotage and flexible approaches to treatment

INFERIOR ALVEOLAR NERVE BLOCK BY INJECTION INTO THE PTERYGOMANDIBULAR SPACE USING GUIDING DEVICES: A SYSTEMATIC REVIEW

The AIM of our research was to analyze and compare different inferior alveolar nerve blocking techniques and the effectiveness of various guiding devices. METHODS: A search was conducted on specialized databases for search and selection of works in which a guiding device for lower alveolar nerve block (IANB) was described. The propriated articles were evaluated and selected in 3 stages for final review based on predefined criteria, followed by a critical evaluation stage. As the research result - various types of IANB guide devices and the results of its using were recorded and analyzed. RESULTS: The systematic review of devices for conducting IANB was done. The success of IANB can be achieved by adjusting the syringe with the anesthetic needle trajectory - it increased the probability of a successful hit in the area of the mandible foramen. Examples of devices in which the syringe is fixed at the moment when the tip of the needle is injected into the medial side of the branch of the lower alveolar nerve are considered. And also, the special techniques based on orientation on the soft tissues are described. However, when creating a device of this type, the following factors must be taken into account: the angle of the needle to the insertion point, the position of the insertion point relative to the anatomical landmarks (taking into account individual characteristics), and the insertion depth. Also, other IANB guiding blockade methods are considered: 3D navigation while local anesthetic injection. Thus, the patient's discomfort, the risk of nerve damage and the risk of unsuccessful mandible anesthesia could be minimized. CONCLUSION: The advantages and disadvantages of these anesthesia methods, the success rate, and patient comfort were analyzed. Prospects for further research in this area were identified