Improved Frequency-selective Filters

This paper gives an account of some techniques for designing recursive frequency-selective filters which can be applied to data sequences of limited duration which may be nonstationary. The designs are based on the Wiener-Kolmogorov theory of signal extraction which employs a statistical model of the processes generating the data. The statistical model may be regarded as an heuristic device which is designed with a view to ensuring that the resulting signal-extraction filters have certain preconceived properties.Signal extraction, Linear filtering, Filter design, Trend estimation, Frequency-domain analysis

IIR Digital Filter Design Using Convex Optimization

Digital filters play an important role in digital signal processing and communication. From the 1960s, a considerable number of design algorithms have been proposed for finite-duration impulse response (FIR) digital filters and infinite-duration impulse response (IIR) digital filters. Compared with FIR digital filters, IIR digital filters have better approximation capabilities under the same specifications. Nevertheless, due to the presence of the denominator in its rational transfer function, an IIR filter design problem cannot be easily formulated as an equivalent convex optimization problem. Furthermore, for stability, all the poles of an IIR digital filter must be constrained within a stability domain, which, however, is generally nonconvex. Therefore, in practical designs, optimal solutions cannot be definitely attained. In this dissertation, we focus on IIR filter design problems under the weighted least-squares (WLS) and minimax criteria. Convex optimization will be utilized as the major mathematical tool to formulate and analyze such IIR filter design problems. Since the original IIR filter design problem is essentially nonconvex, some approximation and convex relaxation techniques have to be deployed to achieve convex formulations of such design problems. We first consider the stability issue. A sufficient and necessary stability condition is derived from the argument principle. Although the original stability condition is in a nonconvex form, it can be appropriately approximated by a quadratic constraint and readily combined with sequential WLS design procedures. Based on the sufficient and necessary stability condition, this approximate stability constraint can achieve an improved description of the nonconvex stability domain. We also address the nonconvexity issue of minimax design of IIR digital filters. Convex relaxation techniques are applied to obtain relaxed design problems, which are formulated, respectively, as second-order cone programming (SOCP) and semidefinite programming (SDP) problems. By solving these relaxed design problems, we can estimate lower bounds of minimum approximation errors, which are useful in subsequent design procedures to achieve real minimax solutions. Since the relaxed design problems are independent of local information, compared with many prevalent design methods which employ local search, the proposed design methods using the convex relaxation techniques have an increased chance to obtain an optimal design

Learning algorithms for adaptive digital filtering

In this thesis, we consider the problem of parameter optimisation in adaptive digital filtering. Adaptive digital filtering can be accomplished using both Finite Impulse Response (FIR) filters and Infinite Impulse Response Filters (IIR) filters. Adaptive FIR filtering algorithms are well established. However, the potential computational advantages of IIR filters has led to an increase in research on adaptive IIR filtering algorithms. These algorithms are studied in detail in this thesis and the limitations of current adaptive IIR filtering algorithms are identified. New approaches to adaptive IIR filtering using intelligent learning algorithms are proposed. These include Stochastic Learning Automata, Evolutionary Algorithms and Annealing Algorithms. Each of these techniques are used for the filtering problem and simulation results are presented showing the performance of the algorithms for adaptive IIR filtering. The relative merits and demerits of the different schemes are discussed. Two practical applications of adaptive IIR filtering are simulated and results of using the new adaptive strategies are presented. Other than the new approaches used, two new hybrid schemes are proposed based on concepts from genetic algorithms and annealing. It is shown with the help of simulation studies, that these hybrid schemes provide a superior performance to the exclusive use of any one scheme

Digital Filter Design Using Improved Artificial Bee Colony Algorithms

Digital filters are often used in digital signal processing applications. The design objective of a digital filter is to find the optimal set of filter coefficients, which satisfies the desired specifications of magnitude and group delay responses. Evolutionary algorithms are population-based meta-heuristic algorithms inspired by the biological behaviors of species. Compared to gradient-based optimization algorithms such as steepest descent and Newton’s like methods, these bio-inspired algorithms have the advantages of not getting stuck at local optima and being independent of the starting point in the solution space. The limitations of evolutionary algorithms include the presence of control parameters, problem specific tuning procedure, premature convergence and slower convergence rate. The artificial bee colony (ABC) algorithm is a swarm-based search meta-heuristic algorithm inspired by the foraging behaviors of honey bee colonies, with the benefit of a relatively fewer control parameters. In its original form, the ABC algorithm has certain limitations such as low convergence rate, and insufficient balance between exploration and exploitation in the search equations. In this dissertation, an ABC-AMR algorithm is proposed by incorporating an adaptive modification rate (AMR) into the original ABC algorithm to increase convergence rate by adjusting the balance between exploration and exploitation in the search equations through an adaptive determination of the number of parameters to be updated in every iteration. A constrained ABC-AMR algorithm is also developed for solving constrained optimization problems.There are many real-world problems requiring simultaneous optimizations of more than one conflicting objectives. Multiobjective (MO) optimization produces a set of feasible solutions called the Pareto front instead of a single optimum solution. For multiobjective optimization, if a decision maker’s preferences can be incorporated during the optimization process, the search process can be confined to the region of interest instead of searching the entire region. In this dissertation, two algorithms are developed for such incorporation. The first one is a reference-point-based MOABC algorithm in which a decision maker’s preferences are included in the optimization process as the reference point. The second one is a physical-programming-based MOABC algorithm in which physical programming is used for setting the region of interest of a decision maker. In this dissertation, the four developed algorithms are applied to solve digital filter design problems. The ABC-AMR algorithm is used to design Types 3 and 4 linear phase FIR differentiators, and the results are compared to those obtained by the original ABC algorithm, three improved ABC algorithms, and the Parks-McClellan algorithm. The constrained ABC-AMR algorithm is applied to the design of sparse Type 1 linear phase FIR filters of filter orders 60, 70 and 80, and the results are compared to three state-of-the-art design methods. The reference-point-based multiobjective ABC algorithm is used to design of asymmetric lowpass, highpass, bandpass and bandstop FIR filters, and the results are compared to those obtained by the preference-based multiobjective differential evolution algorithm. The physical-programming-based multiobjective ABC algorithm is used to design IIR lowpass, highpass and bandpass filters, and the results are compared to three state-of-the-art design methods. Based on the obtained design results, the four design algorithms are shown to be competitive as compared to the state-of-the-art design methods

Single Bin Sliding Discrete Fourier Transform

The conventional method for spectrum analysis is the discrete Fourier transform (DFT), usually implemented using a fast Fourier transform (FFT) algorithm. However, certain applications require an online spectrum analysis only on a subset of M frequencies of an N-point DFT (M<N). In such cases, the use of single-bin sliding DFT (Sb-SDFT) is preferred over the direct application of FFT. The purpose of this chapter is to provide a concise overview of the Sb-SDFT algorithms, analyze their performance, and highlight advantages and limitations. Finally, a technique to mitigate the spectral leakage effect, which arises when using the Sb-SDFT in nonstationary conditions, is presented

Hybrid DDS-PLL based reconfigurable oscillators with high spectral purity for cognitive radio

Analytical, design and simulation studies on the performance optimization of reconfigurable architecture of a Hybrid DDS – PLL are presented in this thesis. The original contributions of this thesis are aimed towards the DDS, the dithering (spur suppression) scheme and the PLL. A new design of Taylor series-based DDS that reduces the dynamic power and number of multipliers is a significant contribution of this thesis. This thesis compares dynamic power and SFDR achieved in the design of varieties of DDS such as Quartic, Cubic, Linear and LHSC. This thesis proposes two novel schemes namely “Hartley Image Suppression” and “Adaptive Sinusoidal Interference Cancellation” overcoming the low noise floor of traditional dithering schemes. The simulation studies on a Taylor series-based DDS reveal an improvement in SFDR from 74 dB to 114 dB by using Least Mean Squares -Sinusoidal Interference Canceller (LM-SIC) with the noise floor maintained at -200 dB. Analytical formulations have been developed for a second order PLL to relate the phase noise to settling time and Phase Margin (PM) as well as to relate jitter variance and PM. New expressions relating phase noise to PM and lock time to PM are derived. This thesis derives the analytical relationship between the roots of the characteristic equation of a third order PLL and its performance metrics like PM, Gardner’s stability factor, jitter variance, spur gain and ratio of noise power to carrier power. This thesis presents an analysis to relate spur gain and capacitance ratio of a third order PLL. This thesis presents an analytical relationship between the lock time and the roots of its characteristic equation of a third order PLL. Through Vieta’s circle and Vieta’s angle, the performance metrics of a third order PLL are related to the real roots of its characteristic equation

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