Optimal design of all-pass variable fractional-delay digital filters

This paper presents a computational method for the optimal design of all-pass variable fractional-delay (VFD) filters aiming to minimize the squared error of the fractional group delay subject to a low level of squared error in the phase response. The constrained optimization problem thus formulated is converted to an unconstrained least-squares (LS) optimization problem which is highly nonlinear. However, it can be approximated by a linear LS optimization problem which in turn simply requires the solution of a linear system. The proposed method can efficiently minimize the total error energy of the fractional group delay while maintaining constraints on the level of the error energy of the phase response. To make the error distribution as flat as possible, a weighted LS (WLS) design method is also developed. An error weighting function is obtained according to the solution of the previous constrained LS design. The maximum peak error is then further reduced by an iterative updating of the error weighting function. Numerical examples are included in order to compare the performance of the filters designed using the proposed methods with those designed by several existing methods

A new method for designing causal stable IIR variable fractional delay digital filters

This paper studies the design of causal stable Farrow-based infinite-impulse response (IIR) variable fractional delay digital filters (VFDDFs), whose subfilters have a common denominator. This structure has the advantages of reduced implementation complexity and avoiding undesirable transient response when tuning the spectral parameter in the Farrow structure. The design of such IIR VFDDFs is based on a new model reduction technique which is able to incorporate prescribed flatness and peak error constraints to the IIR VFDDF under the second order cone programming framework. Design example is given to demonstrate the effectiveness of the proposed approach. © 2007 IEEE.published_or_final_versio

A versatile iterative framework for the reconstruction of bandlimited signals from their nonuniform samples

In this paper, we study a versatile iterative framework for the reconstruction of uniform samples from nonuniform samples of bandlimited signals. Assuming the input signal is slightly oversampled, we first show that its uniform and nonuniform samples in the frequency band of interest can be expressed as a system of linear equations using fractional delay digital filters. Then we develop an iterative framework, which enables the development and convergence analysis of efficient iterative reconstruction algorithms. In particular, we study the Richardson iteration in detail to illustrate how the reconstruction problem can be solved iteratively, and show that the iterative method can be efficiently implemented using Farrow-based variable digital filters with few general-purpose multipliers. Under the proposed framework, we also present a completed and systematic convergence analysis to determine the convergence conditions. Simulation results show that the iterative method converges more rapidly and closer to the true solution (i.e. the uniform samples) than conventional iterative methods using truncation of sinc series. © 2010 The Author(s).published_or_final_versionSpringer Open Choice, 21 Feb 201

Techniques to Improve the Efficiency of Data Transmission in Cable Networks

The cable television (CATV) networks, since their introduction in the late 1940s, have now become a crucial part of the broadcasting industry. To keep up with growing demands from the subscribers, cable networks nowadays not only provide television programs but also deliver two-way interactive services such as telephone, high-speed Internet and social TV features. A new standard for CATV networks is released every five to six years to satisfy the growing demands from the mass market. From this perspective, this thesis is concerned with three main aspects for the continuing development of cable networks: (i) efficient implementations of backward-compatibility functions from the old standard, (ii) addressing and providing solutions for technically-challenging issues in the current standard and, (iii) looking for prospective features that can be implemented in the future standard. Since 1997, five different versions of the digital CATV standard had been released in North America. A new standard often contains major improvements over the previous one. The latest version of the standard, namely DOCSIS 3.1 (released in late 2013), is packed with state-of-the-art technologies and allows approximately ten times the amount of traffic as compared to the previous standard, DOCSIS 3.0 (released in 2008). Backward-compatibility is a must-have function for cable networks. In particular, to facilitate the system migration from older standards to a newer one, the backward compatible functions in the old standards must remain in the newer-standard products. More importantly, to keep the implementation cost low, the inherited backward compatible functions must be redesigned by taking advantage of the latest technology and algorithms. To improve the backward-compatibility functions, the first contribution of the thesis focuses on redesigning the pulse shaping filter by exploiting infinite impulse response (IIR) filter structures as an alternative to the conventional finite impulse response (FIR) structures. Comprehensive comparisons show that more economical filters with better performance can be obtained by the proposed design algorithm, which considers a hybrid parameterization of the filter's transfer function in combination with a constraint on the pole radius to be less than 1. The second contribution of the thesis is a new fractional timing estimation algorithm based on peak detection by log-domain interpolation. When compared with the commonly-used timing detection method, which is based on parabolic interpolation, the proposed algorithm yields more accurate estimation with a comparable implementation cost. The third contribution of the thesis is a technique to estimate the multipath channel for DOCSIS 3.1 cable networks. DOCSIS 3.1 is markedly different from prior generations of CATV networks in that OFDM/OFDMA is employed to create a spectrally-efficient signal. In order to effectively demodulate such a signal, it is necessary to employ a demodulation circuit which involves estimation and tracking of the multipath channel. The estimation and tracking must be highly accurate because extremely dense constellations such as 4096-QAM and possibly 16384-QAM can be used in DOCSIS 3.1. The conventional OFDM channel estimators available in the literature either do not perform satisfactorily or are not suitable for the DOCSIS 3.1 channel. The novel channel estimation technique proposed in this thesis iteratively searches for parameters of the channel paths. The proposed technique not only substantially enhances the channel estimation accuracy, but also can, at no cost, accurately identify the delay of each echo in the system. The echo delay information is valuable for proactive maintenance of the network. The fourth contribution of this thesis is a novel scheme that allows OFDM transmission without the use of a cyclic prefix (CP). The structure of OFDM in the current DOCSIS 3.1 does not achieve the maximum throughput if the channel has multipath components. The multipath channel causes inter-symbol-interference (ISI), which is commonly mitigated by employing CP. The CP acts as a guard interval that, while successfully protecting the signal from ISI, reduces the transmission throughput. The problem becomes more severe for downstream direction, where the throughput of the entire system is determined by the user with the worst channel. To solve the problem, this thesis proposes major alterations to the current DOCSIS 3.1 OFDM/OFDMA structure. The alterations involve using a pair of Nyquist filters at the transceivers and an efficient time-domain equalizer (TEQ) at the receiver to reduce ISI down to a negligible level without the need of CP. Simulation results demonstrate that, by incorporating the proposed alterations to the DOCSIS 3.1 down-link channel, the system can achieve the maximum throughput over a wide range of multipath channel conditions

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

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

Improved IIR Low-Pass Smoothers and Differentiators with Tunable Delay

Regression analysis using orthogonal polynomials in the time domain is used to derive closed-form expressions for causal and non-causal filters with an infinite impulse response (IIR) and a maximally-flat magnitude and delay response. The phase response of the resulting low-order smoothers and differentiators, with low-pass characteristics, may be tuned to yield the desired delay in the pass band or for zero gain at the Nyquist frequency. The filter response is improved when the shape of the exponential weighting function is modified and discrete associated Laguerre polynomials are used in the analysis. As an illustrative example, the derivative filters are used to generate an optical-flow field and to detect moving ground targets, in real video data collected from an airborne platform with an electro-optic sensor.Comment: To appear in Proc. International Conference on Digital Image Computing: Techniques and Applications (DICTA), Adelaide, 23rd-25th Nov. 201