Design of two-dimensional IIR digital filters by using a novel hybrid optimization algorithm

This paper proposes a hybrid optimization algorithm named as BBO–PSO, which is a combination of biogeography-based optimization (BBO) and particle swarm optimization (PSO). In BBO–PSO, the whole population will be split into several subgroups and BBO is employed for local search in each subgroup independently to achieve the different local optima while PSO is employed for global search based on the local optima to achieve the global optimum. The test results on the benchmark functions show that BBO–PSO has powerful search ability with great robustness. Furthermore, the proposed algorithm is applied to the design of the 2-D IIR digital filters and the simulation results show that it outperforms the existing methods on this problem.     

Optimal design of IIR digital filters with robust stability using conic-quadratic-programming updates

In this paper, minimax design of infinite-impulse-response (IIR) filters with prescribed stability margin is formulated as a conic quadratic programming (CQP) problem. CQP is known as a class of well-structured convex programming problems for which efficient interior-point solvers are available. By considering factorized denominators, the proposed formulation incorporates a set of linear constraints that are sufficient and near necessary for the IIR filter to have a prescribed stability margin. A second-order cone condition on the magnitude of each update that ensures the validity of a key linear approximation used in the design is also included in the formulation and eliminates a line-search step. Collectively, these features lead to improved designs relative to several established methods. The paper then moves on to extend the proposed design methodology to quadrantally symmetric two-dimensional (2-D) digital filters. Simulation results for both one-dimensional (1-D) and 2-D cases are presented to illustrate the new design algorithms and demonstrate their performance in comparison with several existing methods.     

Derivation of an adaptive algorithm for IIR digital systems realized by power-wave digital filters

This paper presents a new efficient algorithm for adjusting the coefficients of an adaptive infinite impulse response power-wave digital filter in order to estimate the discrete-time signal y(k) as the recursively filtered version of the signalx(k). To do this, eight different prediction errors are defined which can be computed recursively with respect to model order and time, which leads to similar recursions as for the lattice algorithm [1], where autoregressive processes are considered. These recursions can be implemented as a digital filter which can be separated in ananalysis and asynthesis part, where the latter can be interpreted as a power-wave digital filter [2], [3], [13]. Hence, the stability of this adaptive network is always guaranteed [4]. Furthermore, it is shown that the proposed algorithm can be considered as an extension of the Levinson algorithm [7] for the efficient inversion of a special class of matrices.     

Realization of IIR LDM digital filters

A method is presented of realizing an infinite impulse response (IIR) digital filter (DF) using linear delta modulation (LDM) as a simple analog/digital (A/D) converter. This method makes the realization of IIR digital filters much simpler than that of conventional ones because it does not require hardware multipliers or a pulse code modulation (PCM) A/D converter. Compared to the finite impulse response (FIR) LDMDF, this IIR LDMDF requires significantly less computation time     

Design of IIR digital notch filters

A method is presented for the design of notch filters with specified notch frequency ₀ and 3-dB rejection bandwidthB _t, using a first-order real all-pass filter, wherein the only coefficient is used to control the notch frequency. To control the bandwidth, use is made of a new amplitude change function (ACF), and it is shown that given notch filter specifications can be exactly met thereby. Also, using the ACF, it is shown that stability of the second-order notch filter designs can be improved along with the noise gain.     

Optimal design of transform-based block digital filters using a quadratic criterion

Block digital filtering is a powerful tool to reduce the computational complexity of digital filtering systems. However, due to their block structure, block digital filters (BDFs) are time-varying linear systems, hence, their design is not easy. The most widely spread approaches to BDF design consist of constraining the BDF to be time-invariant (by restricting the design process to a specific subset of possible solutions) and then using conventional filter synthesis techniques. In this paper, we do not restrict the design process, and we propose a simple and optimal matrix-oriented approach to optimize the BDF coefficients. Furthermore, the proposed approach takes profit of the structure of transform-based BDFs to considerably reduce the computational complexity and memory requirements of the design process. Experimental results confirm that as expected, the obtained global distortion is lower than the distortion obtained with a traditional technique such as overlap-save.     

Design of linear-phase IIR digital filters using singularperturbational model reduction

A new technique for the design of a passband linear-phase infinite impulse response (IIR) digital filter is presented. This technique is based on computing orthonormal bases, which span the left and right invariant subspaces associated with the large and small eigenvalues of the cross-Gramian matrix W_c0, which tends to be symmetric and easily constructed. The orthonormal bases are computed by using the ordered real Schur form decomposition, which has been proved to be robust and numerically stable. The proposed technique is illustrated by several examples     

Weighted least-squares approximation of FIR by IIR digital filters

This paper presents a method for the weighted least-squares approximation of finite impulse response (FIR) filters by infinite impulse response (IIR) filters. It is shown, how a solution to this approximation problem can be obtained by solving a related pure least-squares approximation problem. For the latter, we utilize a generalized version of a previously published technique with low computational complexity and guaranteed stability of the IIR filters. Unlike the well-established model-reduction approaches that are carried out in the state space, our method works directly with the numerator and denominator coefficients of the transfer functions. Thus, the influence of finite-precision arithmetic on the results is small. This makes our approach applicable for the approximation of large-order FIR filters and allows the usage of arbitrarily shaped weighting functions. It is shown that our method can successfully be employed to achieve a uniform approximation     

A new approach to the design of complex all-pass IIR digital filters

A new method is proposed for designing complex all-pass IIR filters, the all-pass IIR filters with complex coefficients, in this paper. By minimizing the integration of certain square phase error over interested frequencies, an eigenvector of an appropriate real, symmetric and positive-definite matrix is computed to get the filter coefficients. The stability is achieved by specifying properly the desired phase specifications. If an appropriate iterative process is used, equiripple complex all-pass filter design can be obtained. The method is simple and the performance is comparable to the existing methods. Several examples are presented to demonstrate the effectiveness of the approach.     

Canonic ladder realizations of IIR digital filters

Two new canonic realizations of IIR digital filters age presented. The realizations are derived employing modified continued fraction expansion procedures. Proposed methods also provide alternate derivations to the digital lattice and ladder structures based on two-pair extractions and orthogonal polynomial expansions.     

Frequency domain synthesis of IIR digital filters by means of associated FIR filters

This correspondence describes a synthesis technique for IIR digital filters which allows the use of approximation methods already developed for designing FIR filters. The technique is based on the definition, by means of a suitable transformation, of a FIR filter associated to the desired IIR filter. An example of application is given and the related results are briefly discussed.     

Minimax design of two-channel nonuniform-division filterbanks using IIR allpass filters

The design of two-channel linear-phase nonuniform-division filter (NDF) banks constructed by infinite impulse response (IIR) digital allpass filters (DAFs) in the sense of L/sub /spl infin// error criteria is considered. First, the theory of two-channel NDF bank structures using two IIR DAFs is developed. Then, the design problem is appropriately formulated to result in a simple optimization problem. Utilizing a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the coefficients for the IIR DAFs. The resulting two-channel NDF banks can possess approximately linear-phase response without magnitude distortion. The effectiveness of the proposed technique is achieved by forming an appropriate Chebyshev approximation of a desired phase response and then to find its solution from a linear subspace in a few iterations. Several simulation examples are presented for illustration and comparison.     

基于混合遗传算法的m序列波形优化设计

现代雷达体制多采用大时宽带宽积的m-序列二相编码脉冲压缩波形,解决信号波形优化问题即使信号波形的脉压比在尽量少损失SNR和主瓣宽度的基础上达到极值.对于m-序列,初始寄存器的选取是关键.对于较长的码,传统的优化方法由于运算量过大造成组合爆炸或陷入局部极值而无法找到最优,传统遗传算法也由于初始种群数的规模运算量比较大,将梯度搜索和遗传算法相结合的混合遗传算法很好的解决了这个问题,通过优化m-序列二相码波形的仿真和性能分析验证了该算法的可行性和有效性.     

Lowpass digital filters using least-squared-error design

A method is presented of designing digital filters which give a least-squared-error fit to a polynomial expression. An example is given of a second-order digital-filter approximation to a first-order continuous filter.     

基于人工鱼群算法的IIR数字滤波器设计

将人工鱼群算法（AFSA）用于IIR数字滤波器设计，建立了相应的优化模型，给出了简化的人工鱼群算法及其实现步骤。最后，将该算法用于低通、带通IIR数字滤波器的设计，并与粒子群算法进行了比较。仿真结果证明了AFSA的有效性，并且具有算法灵活、简单，全局收敛性好。收敛速度快的优点。     

Modified canonic ladder realisation of IIR digital filters

Two modified canonic ladder realisations of IIR digital filters are proposed. They are better than those suggested by Neuvo and Mitra for realisability, although the realisations are also derived using modified continued-fraction expansion procedures.     

A design of linear-phased IIR Nyquist filters

This paper discusses a new method of designing linear-phased IIR Nyquist filters with zero intersymbol interference. The filters designed by this method possess linear-phase characteristics and are lower in order than other Nyquist filters designed by existing methods. Expressions are derived for zero-phased IIR Nyquist filters and efficient design methods are examined for them. The opted design method is based on an iteration process, and in each iteration step a modified version of the Remez exchange algorithm is used. In addition, the implementation of the designed zero-phased IIR filters is considered. Finally, the proposed design method is demonstrated through various design examples