Design of low-order linear-phase IIR filters via orthogonalprojection

This paper presents an indirect linear-phase IIR filter design technique based on a reduction of linear-phase FIR filters. The desired filter is obtained by minimizing the L₂ norm of the difference between the original FIR filter and the lower order IIR filter. We first establish a relationship between the Hankel singular values of the discarded part of the FIR filter and the L₂ norm of the corresponding filter approximation error based on model truncation. This result motivates us to propose a simple finite search method that will achieve better approximation results than commonly used truncation methods such as the balanced truncation (BT) and the impulse response gramian (IRG) methods. We then develop an iterative algorithm for finding an optimal IIR filter based on a matrix projection of the original FIR filter. The convergence of the proposed algorithm is established. Filters designed using the proposed algorithm are compared with those obtained by other techniques with respect to the amplitude response and group delay characteristics in the passband. Numerical examples show that the proposed algorithm offers the best performance     

The use of model reduction techniques for designing IIR filterswith linear phase in the passband

A technique to design IIR filters with linear phase in the passband is presented. This technique is based on model reduction of an FIR prototype using frequency weighting to improve the approximation in the transition region. Filters designed using the proposed technique are compared with linear-phase FIR designs and to IIR phase equalized designs with respect to computational complexity and group delay. It is shown that for highly selective filters, the proposed technique offers a good compromise     

Multidimensional IIR filters and robust rational interpolation

It is well-known that IIR filters can have a much lower order than FIR filters with the same performance. On the downside is that the implementation of an IIR filter is an iterative procedure while that of an FIR filter is a one-shot computation. But in higher dimensions IIR filters are definitely more attractive. We offer a technique where the filter’s performance specifications, stability constraints, its convergence speed and a protection against possible adverse effects of perturbations are all included in the design from the start. The technique only needs an off-the-shelf LP solver because the filter is obtained as a Chebyshev center of a convex polytope. The method deals with general non-causal non-separable filters.     

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     

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.     

Broadband Beamforming Using TDL-Form IIR Filters

Conventional broadband beamforming structures make use of finite-impulse-response (FIR) filters in each channel. Large numbers of coefficients are required to retain the desired signal-to-interference-plus-noise-ratio (SINR) performance as the operating bandwidth increases. It has been proven that the optimal frequency-dependent array weighting of broadband beamformers could be better approximated by infinite-impulse-response (IIR) filters. However, some potential problems, such as stability monitoring and sensitivity to quantization errors, of the IIR filters make the implementation of the IIR beamformers difficult. In this paper, new broadband IIR beamformers are proposed to solve these problems. The main contributions of this paper include 1) the Frost-based and generalized sidelobe canceller (GSC)-based broadband beamformers utilizing a kind of tapped-delay-line-form (TDL-form) IIR filters are proposed; 2) the combined recursive Gauss-Newton (RGN) algorithm is designed to compute the feedforward and feedback weights in the Frost-based implementation; and 3) in the GSC-based structure, the unconstrained RGN algorithm is customized for the TDL-form IIR filters in the adaptive beamforming part. Compared with the beamformer using direct-form IIR filters, the new IIR beamformers offer much easier stability monitoring and less sensitivity to the coefficient quantization, while comparable SINR improvement over the conventional FIR beamformer is achieved     

Optical half-band filters

This paper proposes two kinds of novel 2×2 circuit configuration for finite-impulse response (FIR) half-band filters. These configurations can be transformed into each other by a symmetric transformation and their power transmittance is identical. The configurations have only about half the elements of conventional FIR lattice-form filters. We derive a design algorithm for achieving desired power transmittance spectra. We also describe 2×2 circuit configurations for infinite-impulse response (IIR) half-band filters. These configurations are designed to realize arbitrary-order IIR half-band filter characteristics by extending the conventional half-band circuit configuration used in millimeter-wave devices. We discuss their filter characteristics and confirm that they have a power half-band property. We demonstrate design examples including FIR maximally flat half-band filters, an FIR Chebyshev half-band filter, and an IIR elliptic half-band filter     

Least-squares design of IIR filters with prescribed magnitude andphase responses and a pole radius constraint

This paper presents a method for the frequency domain design of infinite impulse response (IIR) digital filters. The proposed method designs filters approximating prescribed magnitude and phase responses. IIR filters of this kind can have approximately linear-phase responses in their passbands, or they can equalize magnitude and phase responses of given systems. In many cases, these filters can be implemented with less memory and with fewer computations per output sample than equivalent finite impulse response (FIR) digital filters. An important feature of the proposed method is the possibility to specify a maximum radius for the poles of the designed rational transfer function. Consequently, stability can be guaranteed, and undesired effects of implementations using fixed-point arithmetic can be alleviated by restricting the poles to keep a prescribed distance from the unit circle. This is achieved by applying Rouche's theorem in the proposed design algorithm. We motivate the use of IIR filters with an unequal number of poles and zeros outside the origin of the complex plane. In order to satisfy simultaneous specifications on magnitude and phase responses, it is advantageous to use IIR filters with only a few poles outside the origin of the z-plane and an arbitrary number of zeros. Filters of this type are a compromise between IIR filters with optimum magnitude responses and phase-approximating FIR filters. We use design examples to compare filters designed by the proposed method to those obtained by other methods. In addition, we compare the proposed general IIR filters with other popular more specialized structures such as FIR filters and cascaded systems consisting of frequency-selective IIR filters and phase-equalizing allpass filters     

Reduced order IIR approximation to FIR digital filters

An algorithm for designing an infinite-impulse-response (IIR) stable filter using a finite-impulse-response (FIR) given filter, with the objective of reducing the delay and order, is described. The design is in the time domain using the least-squares-inverse algorithm, which is briefly described. In this method, the numerator of the approximated filter is part of the FIR filter itself and no calculations and minimization are needed to find the numerator coefficients (except finding the FIR roots). An error analysis between the given FIR and approximated IIR filters is provided. This error analysis enables the designer to fix a design parameter, often unnoted, keeping the energies of the approximated and original filters equal. Results and two illustrative examples are presented     

General IIR optical filter design for WDM applications usingall-pass filters

A general design algorithm is presented for infinite impulse response (IIR) bandpass and arbitrary magnitude response filters that use optical all-pass filters as building blocks. Examples are given for an IIR multichannel frequency selector, an amplifier gain equalizer, a linear square-magnitude response, and a multi-level response. Major advantages are the efficiency of the IIR filter compared to finite impulse response (FIR) filters, the simplicity of the optical architecture, and its tolerance for loss. A reduced set of unique operating states is discussed for implementing a reconfigurable multichannel selection filter     

Frequency domain design of FIR and IIR Laplacian of Gaussian filters for edge detection

This work addresses the design of LoG filters in the frequency domain within a structure formed by the cascade of quasi-Gaussian and discrete Laplacian filters. The main feature of such a structure is that it requires half the number of convolutions of the classical structure in which the LoG transfer function is expressed as the sum of two separable transfer functions of 1-D Gaussian and LoG type. Such a perspective allows one to rephrase the design of IIR and FIR filters for edge detection as a frequency domain approximation problem solvable by standard digital filter design tools. The zero-phase IIR solutions have a good performance at low orders and approximation errors practically independent of the aperture parameter. The characteristics of the nearly linear-phase IIR filters solving the problem suggest the consideration of linear-phase FIR filters with zeros constrained on the unit circle. The use of such filters leads to remarkable computational savings with respect to the filters designed by impulse response sampling. The agreement between the edge values obtained by the filters designed according to the scheme proposed in this work and those obtained by standard techniques is very good.Work carried out with the financial support of the C.N.R.-Progetto Finalizzato Robotica, contract no. 91.01942.PF67.     

FIR filter order reduction: balanced model truncation andHankel-norm optimal approximation

Two different algorithms for approximating FIR by IIR filters are treated: truncation of the balanced model and the Hankel-norm optimal approximation. Both are assessed for approximation fidelity, as well as for intrinsic computational efficiency. Examples show surprisingly good relative performance of the balanced model truncation, suggesting that frequently this method will be operationally preferable     

A fast algorithm for FIR digital filtering with a sum-of-triangles weighting function

A doubly recursive algorithm for time domain convolution with a piecewise linear weighting function is presented that combines the speed of a recursive (IIR) digital filter with the flexibility and ease of design of a nonrecursive (FIR) digital filter. The approach approximates the desired FIR weighting function by a sum-of-triangles weighting function. ForL triangles (or triangle pairs for a linear phase filter) the algorithm is of orderLN. The approximation improves with the number of triangles. A significant advantage of the algorithm compared to FFT filtering or direct convolution is that there is no necessity of a tradeoff between frequency response accuracy and computation time per output point as the data spacing decreases in the filtered signal. The computational complexity is dependent on the number of triangles chosen, not the width of the weighting function, so the algorithm is especially effective for filters with an inherently wide FIR weighting function.     

FIR, Allpass, and IIR Variable Fractional Delay Digital Filter Design

This paper presents two-step design methodologies and performance analyses of finite-impulse response (FIR), allpass, and infinite-impulse response (IIR) variable fractional delay (VFD) digital filters. In the first step, a set of fractional delay (FD) filters are designed. In the second step, these FD filter coefficients are approximated by polynomial functions of FD. The FIR FD filter design problem is formulated in the peak-constrained weighted least-squares (PCWLS) sense and solved by the projected least-squares (PLS) algorithm. For the allpass and IIR FD filters, the design problem is nonconvex and a global solution is difficult to obtain. The allpass FD filters are directly designed as a linearly constrained quadratic programming problem and solved using the PLS algorithm. For IIR FD filters, the fixed denominator is obtained by model reduction of a time-domain average FIR filter. The remaining numerators of the IIR FD filters are designed by solving linear equations derived from the orthogonality principle. Analyses on the relative performances indicate that the IIR VFD filter with a low-order fixed denominator offers a combination of the following desirable properties including small number of denominator coefficients, lowest group delay, easily achievable stable design, avoidance of transients due to nonvariable denominator coefficients, and good overall magnitude and group delay performances especially for high passband cutoff frequency ( ges 0.9pi) . Filter examples covering three adjacent ranges of wideband cutoff frequencies [0.95, 0.925, 0.9], [0.875, 0.85, 0.825], and [0.8, 0.775, 0.75] are given to illustrate the design methodologies and the relative performances of the proposed methods.     

DESIGN OF POLYPHASE WAVE DIGITAL FILTERS WITH APPROXIMATELY LINEAR PHASE

It is well known that IIR digital filters require quite fewer computations,comparedwith FIR filters,in order to meet stringent magnitude specifications when the phase distortioncan be tolerated.An approximately linear phase,however,can be also obtained with the IIRfilter by making use of a technique without increasing the complexity.Based on a certain numberof attenuation zeros in the pass band,a new approach is developed for the design of polyphasewave digital filters with exact magnitude responses and Chebyshev approximation of the desiredphase responses.The minimum number of attenuation zeros is estimated,and some examples areincluded.     

基于FIR与相位补偿IIR滤波器的雷达回波信号处理

FIR与IIR频率选择滤波器的设计,被广泛应用于数字信号处理领域之中。文章以雷达回波信号的数字处理为例,首先分别设计FIR,IIR滤波器完成了对信号特定频率分量的滤除。进而,针对IIR滤波器的非线性相位,基于最优化设计全通系统实现了相位补偿,并对FIR,IIR滤波器进行了综合比较。     

Complex IIR filter design through balance model reduction of FIRprototypes

The author extend the use of the balance model truncation and Hankel-norm optimal approximation to permit close approximation of complex FIR prototypes by IIR filters     

Two-channel IIR QMF banks with approximately linear-phase analysisand synthesis filters

Perfect linear-phase two-channel QMF banks require the use of finite impulse response (FIR) analysis and synthesis filters. Although they are less expensive and yield superior stopband characteristics, perfect linear phase cannot be achieved with stable infinite impulse response (IIR) filters. Thus, IIR designs usually incorporate a postprocessing equalizer that is optimized to reduce the phase distortion of the entire filter bank. However, the analysis and synthesis filters of such an IIR filter bank are not linear phase. In this paper, a computationally simple method to obtain IIR analysis and synthesis filters that possess negligible phase distortion is presented. The method is based on first applying the balanced reduction procedure to obtain nearly allpass IIR polyphase components and then approximating these with perfect allpass IIR polyphase components. The resulting IIR designs already have only negligible phase distortion. However, if required, further improvement may be achieved through optimization of the filter parameters. For this purpose, a suitable objective function is presented. Bounds for the magnitude and phase errors of the designs are also derived. Design examples indicate that the derived IIR filter banks are more efficient in terms of computational complexity than the FIR prototypes and perfect reconstruction FIR filter banks. Although the PR FIR filter banks when implemented with the one-multiplier lattice structure and IIR filter banks are comparable in terms of computational complexity, the former is very sensitive to coefficient quantization effects     

A new method for adaptive IIR filter design based on tabu search algorithm

Adaptive digital filters have proven their worth in a wide range of applications such as channel equalisation, noise reduction, echo cancelling, and system identification. These filters can be broadly classified into two groups: finite impulse–response (FIR) and infinite impulse–response (IIR) filters. IIR filters have become the target of increasing interest because these filters can reduce the filter order significantly as compared to FIR filters. Tabu search is a heuristic optimisation algorithm which has been originally developed for combinatorial optimisation problems. It simulates the general rules of intelligent problem solving and has the ability of discovering the global minima in a multi-modal search space. In this work, a novel method based on tabu search is described for the design of adaptive IIR filters.