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     

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     

Design of linear-phase IIR filters via impulse-response gramians

A new method for the design of a linear-phase infinite-impulse-response (IIR) filter is presented. It involves designing a finite-impulse-response (FIR) filter satisfying the given frequency response specifications and subsequently obtaining a significantly lower order IIR filter using model reduction based on impulse-response gramians. The general outline of the method and a brief overview of the existing linear-phase FIR filter design and model-reduction techniques are presented. The impulse-response gramian and the model-reduction algorithm used are presented. The method is illustrated by design examples and is compared with other methods for the design of linear-phase IIR filters using equalizers     

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.     

Q value analysis of microwave photonic filters

This paper first presents the fundamental principles of the microwave photonic filters.As an example to explain how to implement a microwave photonic filter, a specific finite impulse response (FIR) filter is illustrated.Next, the Q value of the microwave photonic filters is analyzed theoretically, and methods around how to gain high Q value are discussed.Then,divided into FIR filter, first-order infinite impulse response (IIR) filter, and multi-order IIR filter, several novel microwave photonic filters with high Q value are listed and compared.The technical difficulties to get high Q value in first-order IIR filter and multi-order IIR filter are analyzed concretely.Finally, in order to gain higher Q value, a multi-order IIR microwave photonic filter that easily extends its order is presented and discussed.     

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.     

Design of stable, causal, perfect reconstruction, IIR uniform DFTfilter banks

Design procedures for stable, causal and perfect reconstruction IIR parallel uniform DFT filter banks (DFT FBs) are presented. In particular a family of IIR prototype filters is a good candidate for DFT FB, where a tradeoff between frequency selectivity and numerical properties (as measured by the Weyl-Heisenberg frames theory) could be made. Some realizations exhibiting a simple and a massively parallel and modular processing structure making a VLSI implementation very suitable are shown. In addition, some multipliers in the filters (both the analysis and synthesis) could be made; powers or sum of powers of 2, in particular for feedback loops, resulting in a good sensitivity behavior. For these reasons as well as for the use of low order IIR filters (as compared with conventional FIR filters), the overall digital filter bank structure is efficient for high data rate applications. Some design examples are provided     

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 analysis of two-band QMF banks

The two-channel perfect-reconstruction quadrature-mirror-filter banks (PR QMF banks) are analyzed in detail by assuming arbitrary analysis and synthesis filters. Solutions where the filters are FIR or IIR correspond to the fact that a certain function is monomial or nonmonomial, respectively. For the monomial case, the design problem is formulated as a nonlinear constrained optimization problem. The formulation is quite robust and is able to design various two-channel filter banks such as orthogonal and biorthogonal, arbitrary delay, linear-phase filter banks, to name a few. Same formulation is used for causal and stable PR IIR filter bank solutions     

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 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     

A direct approach to H2 optimal deconvolution ofperiodic digital channels

This paper studies the H₂ optimal deconvolution problem for periodic finite impulse response (FIR) and infinite impulse response (IIR) channels. It shows that the H₂ norm of a periodic filter can be directly quantified in terms of periodic system matrices and linear matrix inequalities (LMIs) without resorting to the commonly used lifting technique. The optimal signal reconstruction problem is then formulated as an optimization problem subject to a set of matrix inequality constraints. Under this framework, the optimization of both the FIR and IIR periodic deconvolution filters can be made convex, solved using the interior point method, and computed by using the Matlab LMI Toolbox. The robust deconvolution problem for periodic FIR and IIR channels with polytopic uncertainties are further formulated and solved, also by convex optimization and the LMIs. Compared with the lifting approach to the design of periodic filters, the proposed approach is simpler yet more powerful in dealing with multiobjective deconvolution problems and channel uncertainties, especially for IIR deconvolution filter design. The obtained solutions are applied to the design of an optimal filterbank yielding satisfactory performance     

Analysis and design of periodically time-varying IIR filters, withapplications to transmultiplexing

Fundamental constraints on the form of infinite impulse response (IIR) periodically time-varying (PTV) filters are identified, and a design technique with well-defined error and stability characteristics based on those constraints is presented. The design technique is based on the selection of poles and zeros within the time-invariant filter banks of equivalent PTV filter analysis structures. A simple example is presented to illustrate the design method, which implements the IIR PTV as a time-invariant all-feedback IIR filter of the form 1/D(z^P) cascaded with an finite impulse response (FIR) PTV filter. An application of IIR PTV filters to telecommunications transmultiplexing is presented to illustrate the design method and for comparison to an existing PTV design method. The computational complexity of the resulting system compares favorably with that of existing transmultiplexers     

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     

Maxflat Fractional Delay IIR Filter Design

Fractional delay (FD) filters are an important class of digital filters and are useful in various signal processing applications. This paper discusses a design problem of FD infinite-impulse-response (IIR) filters with the maxflat frequency response in frequency domain. First, a flatness condition of FD filters at an arbitrarily specified frequency point is described, and then a system of linear equations is derived from the flatness condition. Therefore, a set of filter coefficients can be easily obtained by solving this system of linear equations. For a special case in which the frequency response is required to be maxflat at omega = 0 or pi , a closed-form expression for its filter coefficients is derived by solving a linear system of Vandermonde equations. It is also shown that the existing maxflat FD finite-impulse-response (FIR) and IIR filters are special cases of the FD IIR filters proposed in this paper. Finally, some examples are presented to demonstrate the effectiveness of the proposed filters.     

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。     

Design and Factorization of Two-Channel Perfect Reconstruction Filter Banks with Causal-Stable IIR Filters

In this paper, new design and factorization methods of two-channel perfect reconstruction (PR) filter banks (FBs) with casual-stable IIR filters are introduced. The polyphase components of the analysis filters are assumed to have an identical denominator in order to simplify the PR condition. A modified model reduction is employed to derive a nearly PR causal-stable IIR FB as the initial guess to obtain a PR IIR FB from a PR FIR FB. To obtain high quality PR FIR FBs for carrying out model reduction, cosine-rolloff FIR filters are used as the initial guess to a nonlinear optimization software for solving to the PR solution. A factorization based on the lifting scheme is proposed to convert the IIR FB so obtained to a structurally PR system. The arithmetic complexity of this FB, after factorization, can be reduced asymptotically by a factor of two. Multiplier-less IIR FB can be obtained by replacing the lifting coefficients with the canonical signal digitals (CSD) or sum of powers of two (SOPOT) coefficients.     

Low-power digital filtering using approximate processing

We present an algorithmic approach to the design of low-power frequency-selective digital filters based on the concepts of adaptive filtering and approximate processing. The proposed approach uses a feedback mechanism in conjunction with well-known implementation structures for finite impulse response (FIR) and infinite impulse response (IIR) digital filters. Our algorithm is designed to reduce the total switched capacitance by dynamically varying the filter order based on signal statistics. A factor of 10 reduction in power consumption over fixed-order filters is demonstrated for the filtering of speech signals     

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