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

Filtering Nonuniformly Sampled Grid-Based Signals

This paper presents an example application of digital alias-free signal processing, where a sequence of irregularly spaced, yet uniformly gridded, samples of a bandlimited discrete-time signal is filtered by using an oversampled finite impulse response filter. The mathematical model of the proposed filter is introduced, and a new interpolation formula for calculating the convolution operation of the filter, based on nonuniform sampling, is derived. In addition, uniform grid versions of Total Random, Stratified and Antithetical Stratified random sampling techniques are demonstrated. We carry out numerical comparison between these techniques and the proposed one in terms of Fourier transform estimates of the filtered output signal. The proposed interpolation technique shows enhancements over other sampling techniques after certain number of sampling points. Furthermore, it has a faster uniform convergence rate of the normalized root mean squared error than other techniques

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

The Impact of Cyber Bullying on the Psychological Well-being of University Students: A Study in Jordanian Universities,

The study examined the impact of Cyberbullying on Jordanian university students\u27 psychological well-being. The correlational descriptive method was used with a sample of 750 male and female students from Jordanian universities. Findings revealed a low degree of cyberbullying\u27s effect on their psychological well-being. No significant differences were found based on gender, college, cumulative GPA, or type of university. However, first-year students experienced higher levels of impact. The researcher recommended raising awareness about cyberbullying consequences, utilizing punishments as deterrents, and implementing preventive mechanisms

Implementing health technology assessment in Kuwait: a qualitative study of perceived barriers and facilitators

Objectives: This study sought to explore main barriers and facilitators to implementing health technology assessment (HTA) in Kuwait from the perspective of key stakeholders. Methods: Semi-structured qualitative interviews were conducted with ten key stakeholders: seven healthcare providers working at various departments of the Kuwaiti Ministry of Health (MOH), and three academics with substantial experience in teaching HTA or related fields. Interviews were conducted face-to-face, audio-recorded, and transcribed verbatim. Data were analyzed using an inductive thematic approach. Results: Participating stakeholders reported several factors that might act as a barrier to building HTA in Kuwait: minimal awareness of HTA, lack of institutional and human capacity, a fragmented healthcare system, poor communication between researchers and policy makers, the country's wealth, politics, as well as data quality, availability, and sharing. Institutionalizing HTA as a politically empowered body, enforcing its recommendation by law, and benefiting from neighboring countries' experiences were suggested as possible ways to move forward. Conclusion: Studies exploring the unique challenges that high-income developing countries may face in implementing HTA are still scarce. The results of this study are consistent with evidence coming from other developing countries, while also suggesting that the abundance of financial resources in the country is a double-edged sword; it has the potential to facilitate the development of HTA capacity, but also hinders recognizing the need for it

Implementation Research in Community Based Rehabilitation

Implementation research (IR) is a non-traditional methodology of research that enables the examination of application of multiple interventions within the complexities of the real-world, and the generation of solutions for emergent needs, especially in countries of low-moderate income. Community-based rehabilitation (CBR) is an evolving field of practice that lacks research traditions. Evidence guiding the practice of healthcare professionals in CBR and supporting its implementation is fragmented. A review of the literature was conducted to identify research studies pertinent to the employment of IR in CBR. This paper demonstrates that the principles of IR resonate with the principles of inclusion, equality, empowerment and partnership of CBR. It also posits that IR can serve as a research tradition to underpin and guide the conduction of research studies in CBR, and to provide the necessary evidence to support its accountability

Achievement Motivation among School Principals in the Southern Badia

This study aimedto identify the level of achievement motivation among school principals in the Southern Badia in the light of the variables of (gender, years of experience, educational qualification). The study sample consisted of all the school principals in the directorate of education in SouthernBadia, withtotal of (77) male and female principals during the first semester (2021-2022). The researcher developed a scale to measure achievement motivation based on the theoretical literature and previous studies. The study instrument consisted of two parts: the first measured the personal vocational variables, including gender, educational qualification, and years of experience, while the second measured the level of achievement motivation among school principals in the Southern Badia.The instrument was distributed into(5) dimensions:achievement behavior, perseverance in efforts, work orientation, work pressure, and ambition. The results revealed that the level of achievement motivation, achievement behavior, and persistence among school principals in the Southern Badia was medium. The results revealed that there are no statistically significant differences in achievement motivation attributed to the variable of gender and educational qualification among them, while there are statistically significant differences in achievement motivation attributed to the variable of years of experience. Keywords: achievement motivation, school principal. DOI: 10.7176/JEP/14-10-04 Publication date: April 30th 202