Design of digital differentiators

A digital differentiator simply involves the derivation of an input signal. This work includes the presentation of first-degree and second-degree differentiators, which are designed as both infinite-impulse-response (IIR) filters and finite-impulse-response (FIR) filters. The proposed differentiators have low-pass magnitude response characteristics, thereby rejecting noise frequencies higher than the cut-off frequency. Both steady-state frequency-domain characteristics and Time-domain analyses are given for the proposed differentiators. It is shown that the proposed differentiators perform well when compared to previously proposed filters. When considering the time-domain characteristics of the differentiators, the processing of quantized signals proved especially enlightening, in terms of the filtering effects of the proposed differentiators. The coefficients of the proposed differentiators are obtained using an optimization algorithm, while the optimization objectives include magnitude and phase response. The low-pass characteristic of the proposed differentiators is achieved by minimizing the filter variance. The low-pass differentiators designed show the steep roll-off, as well as having highly accurate magnitude response in the pass-band. While having a history of over three hundred years, the design of fractional differentiator has become a ‘hot topic’ in recent decades. One challenging problem in this area is that there are many different definitions to describe the fractional model, such as the Riemann-Liouville and Caputo definitions. Through use of a feedback structure, based on the Riemann-Liouville definition. It is shown that the performance of the fractional differentiator can be improved in both the frequency-domain and time-domain. Two applications based on the proposed differentiators are described in the thesis. Specifically, the first of these involves the application of second degree differentiators in the estimation of the frequency components of a power system. The second example concerns for an image processing, edge detection application

Digital Filters and Signal Processing

Digital filters, together with signal processing, are being employed in the new technologies and information systems, and are implemented in different areas and applications. Digital filters and signal processing are used with no costs and they can be adapted to different cases with great flexibility and reliability. This book presents advanced developments in digital filters and signal process methods covering different cases studies. They present the main essence of the subject, with the principal approaches to the most recent mathematical models that are being employed worldwide

Digital Filter Design Using Improved Teaching-Learning-Based Optimization

Digital filters are an important part of digital signal processing systems. Digital filters are divided into finite impulse response (FIR) digital filters and infinite impulse response (IIR) digital filters according to the length of their impulse responses. An FIR digital filter is easier to implement than an IIR digital filter because of its linear phase and stability properties. In terms of the stability of an IIR digital filter, the poles generated in the denominator are subject to stability constraints. In addition, a digital filter can be categorized as one-dimensional or multi-dimensional digital filters according to the dimensions of the signal to be processed. However, for the design of IIR digital filters, traditional design methods have the disadvantages of easy to fall into a local optimum and slow convergence. The Teaching-Learning-Based optimization (TLBO) algorithm has been proven beneficial in a wide range of engineering applications. To this end, this dissertation focusses on using TLBO and its improved algorithms to design five types of digital filters, which include linear phase FIR digital filters, multiobjective general FIR digital filters, multiobjective IIR digital filters, two-dimensional (2-D) linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters. Among them, linear phase FIR digital filters, 2-D linear phase FIR digital filters, and 2-D nonlinear phase FIR digital filters use single-objective type of TLBO algorithms to optimize; multiobjective general FIR digital filters use multiobjective non-dominated TLBO (MOTLBO) algorithm to optimize; and multiobjective IIR digital filters use MOTLBO with Euclidean distance to optimize. The design results of the five types of filter designs are compared to those obtained by other state-of-the-art design methods. In this dissertation, two major improvements are proposed to enhance the performance of the standard TLBO algorithm. The first improvement is to apply a gradient-based learning to replace the TLBO learner phase to reduce approximation error(s) and CPU time without sacrificing design accuracy for linear phase FIR digital filter design. The second improvement is to incorporate Manhattan distance to simplify the procedure of the multiobjective non-dominated TLBO (MOTLBO) algorithm for general FIR digital filter design. The design results obtained by the two improvements have demonstrated their efficiency and effectiveness

Synthesis methods for linear-phase FIR filters with a piecewise-polynomial impulse response

his thesis concentrates on synthesis methods for linear-phase finite-impulse response filters with a piecewise-polynomial impulse response. One of the objectives has been to find integer-valued coefficients to efficiently implement filters of the piecewise-polynomial impulse response approach introduced by Saram¨aki and Mitra. In this method, the impulse response is divided into blocks of equal length and each block is created by a polynomial of a given degree. The arithmetic complexity of these filters depends on the polynomial degree and the number of blocks. By using integer-valued coefficients it is possible to make the implementation of the subfilters, which generates the polynomials, multiplication-free. The main focus has been on finding computationally-efficient synthesis methods by using a piecewise-polynomial and a piecewise-polynomial-sinusoidal impulse responses to make it possible to implement high-speed, low-power, highly integrated digital signal processing systems. The earlier method by Chu and Burrus has been studied. The overall impulse response of the approach proposed in this thesis consists of the sum of several polynomial-form responses. The arithmetic complexity depends on the polynomial degree and the number of polynomial-form responses. The piecewise-polynomial-sinusoidal approach is a modification of the piecewise-polynomial approach. The subresponses are multiplied by a sinusoidal function and an arbitrary number of separate center coefficients is added. Thereby, the arithmetic complexity depends also on the number of complex multipliers and separately generated center coefficients. The filters proposed in this thesis are optimized by using linear programming methods

Discrete-time differentiators: design and comparative analysis

This work deals with the problem of online differentiation of noisy signals. In this context, several types of differentiators including linear, sliding-mode based, adaptive, Kalman, and ALIEN differentiators are studied through mathematical analysis and numerical experiments. To resolve the drawbacks of the exact differentiators, new implicit and semi-implicit discretization schemes are proposed in this work to suppress the digital chattering caused by the wrong time-discretization of set-valued functions as well as providing some useful properties, e.g., finite-time convergence, invariant sliding-surface, exactness. A complete comparative analysis is presented in the manuscript to investigate the behavior of the discrete-time differentiators in the presence of several types of noises, including white noise, sinusoidal noise, and bell-shaped noise. Many details such as quantization effect and realistic sampling times are taken into account to provide useful information based on practical conditions. Many comments are provided to help the engineers to tune the parameters of the differentiators

Digital Filters

The new technology advances provide that a great number of system signals can be easily measured with a low cost. The main problem is that usually only a fraction of the signal is useful for different purposes, for example maintenance, DVD-recorders, computers, electric/electronic circuits, econometric, optimization, etc. Digital filters are the most versatile, practical and effective methods for extracting the information necessary from the signal. They can be dynamic, so they can be automatically or manually adjusted to the external and internal conditions. Presented in this book are the most advanced digital filters including different case studies and the most relevant literature

Linear Phase FIR Digital Filter Design Using Differential Evolution Algorithms

Digital filter plays a vital part in digital signal processing field. It has been used in control systems, aerospace, telecommunications, medical applications, speech processing and so on. Digital filters can be divided into infinite impulse response filter (IIF) and finite impulse response filter (FIR). The advantage of FIR is that it can be linear phase using symmetric or anti-symmetry coefficients. Besides traditional methods like windowing function and frequency sampling, optimization methods can be used to design FIR filters. A common method for FIR filter design is to use the Parks-McClellan algorithm. Meanwhile, evolutional algorithm such as Genetic Algorithm (GA), Particle Swarm Optimization (PSO) [2], and Differential Evolution (DE) have shown successes in solving multi-parameters optimization problems. This thesis reports a comparison work on the use of PSO, DE, and two modified DE algorithms from [18] and [19] for designing six types of linear phase FIR filters, consisting of type1 lowpass, highpass, bandpass, and bandstop filters, and type2 lowpass and bandpass filters. Although PSO has been applied in this field for some years, the results of some of the designs, especially for high-dimensional filters, are not good enough when comparing with those of the Parks-McClellan algorithm. DE algorithms use parallel search techniques to explore optimal solutions in a global range. What’s more, when facing higher dimensional filter design problems, through combining the knowledge acquired during the searching process, the DE algorithm shows obvious advantage in both frequency response and computational time

Towards joint communication and sensing (Chapter 4)

Localization of user equipment (UE) in mobile communication networks has been supported from the early stages of 3rd generation partnership project (3GPP). With 5th Generation (5G) and its target use cases, localization is increasingly gaining importance. Integrated sensing and localization in 6th Generation (6G) networks promise the introduction of more efficient networks and compelling applications to be developed

Design and Implementation of an RF Front-End for Software Defined Radios

Software Defined Radios have brought a major reformation in the design standards for radios, in which a large portion of the functionality is implemented through pro­ grammable signal processing devices, giving the radio the ability to change its op­ erating parameters to accommodate new features and capabilities. A software radio approach reduces the content of radio frequency and other analog components of the traditional radios and emphasizes digital signal processing to enhance overall receiver flexibility. Field Programmable Gate Arrays (FPGA) are a suitable technology for the hardware platform as they offer the potential of hardware-like performance coupled with software-like programmability. Software defined radio is a very broad field, encompassing the design of various technologies all the way from the antenna to RF, IF, and baseband digital design. The RF section primarily consists of analog hardware modules. The IF and baseband sections are primarily digital. It is the general process of the radio to convert the incoming signal from RF to IF and then IF to baseband for better signal processing system. In this thesis, some of major building blocks of a Software defined radio are de­ signed and implemented using FPGAs. The design of a Digital front end, which provides the bridge between the baseband and analog RF portions of a wireless receiver, is synthesized. The Digital front end receiver consists of a digital down converter(DDC) which in turn comprises of a direct digital frequency synthesizer (DDFS), a phase accumulator and a low pass filter. The signal processing block of the DDFS is executed using Co-ordinate Rotation Digital Computer (CORDIC) iii Abstract algorithm. Cascaded-Integrator-Comb filters (CIC) are implemented for changing the sample rate of the incoming data. Application of a DDC includes software ra­ dios, multicarrier, multimode digital receivers, micro and pico cell systems,broadband data applications, instrumentation and test equipment and in-building wireless tele­ phony. Also, in this thesis, interfaces for connecting Texas Instruments high speed and high resolution Analog-to-Digital converters (ADC) and Digital-to-Analog converters (DAC) with Xilinx Virtex-5 FPGAs are also implemented and demonstrated