Dsign of I-D Recursive Digital Filters With Linear Phase Using Two All-Pass Filters With/Without Integer Coefficients

Digital signal processing is becoming increasingly important, and is finding applications in speech processing and telecommunications in the area of 1-D signal processing. One of the important branches 1n digital signal processing 1s digital filtering. Among the numbers of structure of digital filters, the recursive(IIR) filter is known for its computational efficiency compared to the FIR counterparts. In this thesis, an alternative approach to the direct design of 1-D recursive digital filters satisfying prescribed magnitude specifications with or without constant group delay characteristic using two all-pass filters is presented. It is known that, by this approach, the most computationally efficient realization can be obtained among IIR filters for meeting the filter specifications. The method uses unconstrained optimization techniques for the filter design to approximate both the group delay and the magnitude response of the desired filter simultaneously if the constant group delay characteristic is required. Two different approaches are chosen for the stability of the filter. In the first approach, a new stability test is used to generate the stable polynomials. In the second approach, one-variable Hurwitz polynomials(HPs) using properties of positive definite matrices are generated. Bilinear transformations are applied to the HPs to obtain the stable polynomials in z domain. The polynomials generated using the approaches explained above are imposed on the filter\u27s denominator polynomials through the variable subs ti tut ion method, hence ensuring the stability .of the designed filter. The designed filters using this method are stable in nature and neither stability check nor stabilization procedure is required. To illustrate the usefulness of the technique, the results obtained are compared with a well known direct method design using a general 1-D IIR transfer function. Once the infinite precision filter is obtained, through a procedure based on discretization and reoptimization technique we discretize all coefficients to integer values. By this algorithm, the error caused by truncating the filter coefficients is minimized. Examples are given with comparisons in order to demonstrate the usefulness of the algorithm

A semi-definite programming (SDP) method for designing IIR sharp cut-off digital filters using frequency-response masking

IEEE International Symposium on Circuits and Systems Proceedings, Vancouver, Canada, 23-26 May 2004This paper studies the design of frequency response masking (FRM) filters with infinite duration impulse response (IIR) model and masking sub-filters. They are useful in realizing sharp cutoff digital filters with low passband delays. The designs of the model and masking filters are carried out by means of semidefinite programming (SDP) and model order reduction. Design results show that low complexity FRM filters with low passband delay can be obtained.published_or_final_versio

On the eigenfilter design method and its applications: a tutorial

The eigenfilter method for digital filter design involves the computation of filter coefficients as the eigenvector of an appropriate Hermitian matrix. Because of its low complexity as compared to other methods as well as its ability to incorporate various time and frequency-domain constraints easily, the eigenfilter method has been found to be very useful. In this paper, we present a review of the eigenfilter design method for a wide variety of filters, including linear-phase finite impulse response (FIR) filters, nonlinear-phase FIR filters, all-pass infinite impulse response (IIR) filters, arbitrary response IIR filters, and multidimensional filters. Also, we focus on applications of the eigenfilter method in multistage filter design, spectral/spacial beamforming, and in the design of channel-shortening equalizers for communications applications

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

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

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

Computer-Aided Design of Switched-Capacitor Filters

This thesis describes a series of computer methods for the design of switched-capacitor filters. Current software is greatly restricted in the types of transfer function that can be designed and in the range of filter structures by which they can be implemented. To solve the former problem, several new filter approximation algorithms are derived from Newton's method, yielding the Remez algortithm as a special case (confirming its convergency properties). Amplitude responses with arbitrary passband shaping and stopband notch positions are computed. Points of a specified degree of tangency to attenuation boundaries (touch points) can be placed in the response, whereby a family of transfer functions between Butterworth and elliptic can be derived, offering a continuous trade-off in group delay and passive sensitivity properties. The approximation algorithms have also been applied to arbitrary group delay correction by all-pass functions. Touch points form a direct link to an iterative passive ladder design method, which bypasses the need for Hurwitz factorisation. The combination of iterative and classical synthesis methods is suggested as the best compromise between accuracy and speed. It is shown that passive ladder prototypes of a minimum-node form can be efficiently simulated by SC networks without additional op-amps. A special technique is introduced for canonic realisation of SC ladder networks from transfer functions with finite transmission at high frequency, solving instability and synthesis difficulties. SC ladder structures are further simplified by synthesising the zeros at +/-2fs which are introduced into the transfer function by bilinear transformation. They cause cancellation of feedthrough branches and yield simplified LDI-type SC filter structures, although based solely on the bilinear transform. Matrix methods are used to design the SC filter simulations. They are shown to be a very convenient and flexible vehicle for computer processing of the linear equations involved in analogue filter design. A wide variety of filter structures can be expressed in a unified form. Scaling and analysis can readily be performed on the system matrices with great efficiency. Finally, the techniques are assembled in a filter compiler for SC filters called PANDDA. The application of the above techniques to practical design problems is then examined. Exact correction of sinc(x), LDI termination error, pre-filter and local loop telephone line weightings are illustrated. An optimisation algorithm is described, which uses the arbitrary passband weighting to predistort the transfer function for response distortions. Compensation of finite amplifier gain-bandwidth and switch resistance effects in SC filters is demonstrated. Two commercial filter specifications which pose major difficulties for traditional design methods are chosen as examples to illustrate PANDDA's full capabilities. Significant reductions in order and total area are achieved. Finally, test results of several SC filters designed using PANDDA for a dual-channel speech-processing ASIC are presented. The speed with which high-quality, standard SC filters can be produced is thus proven

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

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