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.     

Designing IIR filters with a given 3-dB point

Often in infinite impulse response (IIR) filter design, our critical design parameter is the cutoff frequency at which the filter's power decays to half (-3 dB) the nominal passband value. This article presents techniques that aid in the design of discrete-time Chebyshev and elliptic filters given a 3-dB attenuation frequency point. These techniques place Chebyshev and elliptic filters on the same footing as Butterworth filters, which traditionally have been designed for a given 3-dB point. The result is that it is easy to replace a Butterworth design with either a Chebyshev or an elliptic filter of the same order and obtain a steeper rolloff at the expense of some ripple in the passband and/or stopband of the filter.     

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     

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.     

Logarithmic wavelength demultiplexers

A general approach for a full 1 /spl times/ N demultiplexer using a tree of filter stages is proposed. The device architecture is compact, requiring at least N - 1 filter stages, and flexible, as each filter stage can be arbitrarily designed, with the only constraint of the half-band power property. The filters can be realized using any optical filtering techniques as thin-film interference, Bragg gratings, or planar delay-line circuits. The performances of the proposed architecture are illustrated with respect to different lattice-form finite impulse response (FIR) and infinite impulse response (IIR) filter stages, showing that the demultiplexer inherently presents low crosstalk and flat passband. A design example of a 1 /spl times/ 4 demultiplexer consisting of three all-pass (AP) filters is compared with a generalized Mach-Zehnder interferometer (MZI) with four AP filters in its arms, showing that the two approaches achieve similar results.     

Optimal Use of Some Classical Approximations in Filter Design

The classical Butter worth, Chebyshev and Elliptic (Cauer) low-pass filter approximations can be used in the design of analog and IIR digital filters in such a way as to obtain passband, stopband and transition band optimized filters at no order cost. The exact analytical relationships for such an optimal deployment of these approximations are developed and presented in this paper and their use is demonstrated through design examples.     

Selective Digital Filters with Linear Phase

A method for synthesis of digital bandpass and bandstop filters obtained by parallel connection of two allpass networks, is considered. A procedure is based on allpass network linear phase approximation at three levels in mini-max sense, which enables obtaining of selectivedigital filters in form of elliptic filters with linear phase in both passband and stopband.     

Interpolated LIR Mth-band filter design with allpass subfilters

We propose a new allpass-based structure for the IIR Mth-and 2Mth-band filters. These filters consist of M allpass filters and an interpolation filter (sum of two allpasses). Consequently, the proposed structure is very efficient in implementation. By choosing the allpass phase appropriately, the resulting phase response of the IIR Mth-band filter becomes approximately linear. An example is designed and compared with FIR Mth-band filters     

Design and multiplier-less implementation of a class of two-channel PR FIR filterbanks and wavelets with low system delay

A new method for designing two-channel PR FIR filterbanks with low system delay is proposed. It is based on the generalization of the structure previously proposed by Phoong et al. (1995) Such structurally PR filterbanks are parameterized by two functions (/spl beta/(z) and /spl alpha/(z)) that can be chosen as linear-phase FIR or allpass functions to construct FIR/IIR filterbanks with good frequency characteristics. The case of using identical /spl beta/(z) and /spl alpha/(z) was considered by Phoong et al. with the delay parameter M chosen as 2N-1. In this paper, the more general ease of using different nonlinear-phase FIR functions for /spl beta/(z) and /spl alpha/(z) is studied. As the linear-phase constraint is relaxed, the lengths of /spl beta/(z) and /spl alpha/(z) are no longer restricted by the delay parameters of the filterbanks. Hence, higher stopband attenuation can still be achieved at low system delay. The design of the proposed low-delay filterbanks is formulated as a complex polynomial approximation problem, which can be solved by the Remez exchange algorithm or analytic formula with very low complexity. In addition, the orders and delay parameters can be estimated from the given filter specifications using a simple empirical formula. Therefore, low-delay two-channel PR filterbanks with flexible stopband attenuation and cutoff frequencies can be designed using existing filter design algorithms. The generalization of the present approach to the design of a class of wavelet bases associated with these low-delay filterbanks and its multiplier-less implementation using the sum of powers-of-two coefficients are also studied.     

Optimal design of digital IIR filters by using hybrid taguchi genetic algorithm

A hybrid Taguchi genetic algorithm (HTGA) is applied in this paper to solve the problem of designing optimal digital infinite-impulse response (IIR) filters. The HTGA approach is a method of combining the traditional GA (TGA), which has a powerful global exploration capability, with the Taguchi method, which can exploit the optimum offspring. The Taguchi method is inserted between crossover and mutation operations of a TGA. Based on minimizing the L/sub p/-norm approximation error and minimizing the ripple magnitudes of both passband and stopband, a multicriterion combination is employed as the design criterion to obtain the optimal IIR filter that can fit different performance requirements. The proposed HTGA approach is effectively applied to solve the multiparameter and multicriterion optimization problems of designing the digital low-pass (LP), high-pass (HP), bandpass (BP), and bandstop (BS) filters. In these studied problems, there are many parameters and numerous local optima so that these studied problems are challenging enough for evaluating the performances of any proposed GA-based approaches. The computational experiments show that the proposed HTGA approach can obtain better digital IIR filters than the existing GA-based method reported recently in the literature.     

一种设计IIR数字滤波器的参数化方法

 基于连续时间状态空间结构和广义双线性变换,提出了一种设计无限冲激响应(IIR)数字滤波器的参数化方法.优点是稳定区域包含了整个参数空间,因此可以采用无约束优化方法.给出了仿真实例,并与已有的设计方法进行了比较,其通带波动、阻带衰减、群迟延等性能更为优越.     

Periodic stepped-impedance ring resonator (PSIRR) bandpass filter with a miniaturized area and desirable upper stopband characteristics

A periodic stepped-impedance ring resonator (PSIRR) is proposed to design dual-mode bandpass filters with a miniaturized area and desirable upper stopband characteristics. Design parameters of a PSIRR include impedance ratio R of the hi-Z to low-Z sections, their lengths, and number of impedance steps 2N. The resonant characteristics of PSIRRs with various N and R values are investigated by both the transmission-line theory and electromagnetic simulation. Proper choice of the above parameters leads to an optimal reduction of circuit area and extension of upper rejection bandwidth. Two extra transmission zeros exist in the upper stopband and are tunable via changing the arm lengths of the line-to-ring coupling structure. Realized by the standard microstrip technology, the dual-mode PSIRR bandpass filter has not only the first spurious response at higher than 3.7/spl times/ the passband frequency, but also an area reduction of better than 60% against a conventional ring filter. Experimental results of several fabricated circuits validate the analysis and theoretical prediction.     

Complex notch filter design using allpass filter

Complex coefficient IIR notch filter design problems are investigated. The specification of a notch filter is first transformed into that of an allpass filter. An effective approach to the design of this desired allpass filter is developed. The realisation of the proposed notch filter is equivalent to the realisation of an allpass filter. Owing to the mirror-image symmetry relation between the numerator and denominator polynomials of allpass filters, the notch filter can be realised by a computationally efficient lattice structure with very low sensitivity     

Parallel-coupled line filters with enhanced stopband performances

A new class of parallel-coupled line filters with broad stopband response is introduced. The design is based on the synthesis of bandpass prototypes with pre-defined upper stopband characteristics. The new filters have uniform- and stepped-impedance resonators, some of which are loaded by open-circuited stubs at their open-circuited ends. A seventh-order filter implementation is presented with a fundamental passband centered at 1 GHz. The measured wide-band transmission characteristic of the filter demonstrated a broad upper stopband and was in agreement with simulations. The performance of the new filter is also compared with the characteristic of a conventionally designed filter to highlight the advantages of the proposed design method.     

Design of some 2-D filters through the transformation technique

The transformation technique is a powerful tool for designing 2-D FIR filters. However, it is not useful for the design of specially shaped filters with passband/stopband regions not centred around the origin. The authors extend this technique to design two types of filters. A notch filter has a stopband centred about a small region in the 2-D frequency plane. The authors propose an extension to the transformation technique with the windowing concept to achieve the design of notch filters. A directional filter has a passband extending fully along a straight line passing through the origin. The transformation technique is further extended to yield such directional filters. Design and application examples for both these filters are also presented     

基于SIW技术的毫米波滤波器研究与设计

基于基片集成波导（substrate integrated waveguide,SIW）结构设计了两款四阶的耦合带通滤波器,使用三维全波电磁场仿真软件HFSS对设计的两款滤波器进行了仿真设计和优化.由仿真结果分析得出,两款滤波器的工作频率均位于毫米波频段.第一款SIW滤波器实现了切比雪夫型响应,中心频率为20 GHz,带宽为2 GHz,通带内的插入损耗低于1.5 dB,回波损耗低于-20 dB,在阻带中对信号的衰减程度可以达到50 dB.第二款SIW滤波器实现了准椭圆函数型的响应,中心频率为29.1 GHz,带宽为300 MHz,通带内的插入损耗低于1 dB,回波损耗低于-20 dB,在通带到阻带的过渡中实现了两个陷波点.仿真结果表明,在毫米波滤波器设计中引入SIW结构,有利于优化滤波器尺寸,得到较好的滤波器性能指标,是毫米波滤波器发展的一个重要方向.     

Design of a 2-pole LTCC filter for wireless communications

This letter outlines the designing and manufacture of a miniaturized bandpass filter realized by low-temperature cofired ceramic (LTCC) technology for wireless products. The bandpass filter with a central frequency of 1950 MHz and a 5% passband is designed as a three-dimensional (3-D) structure based on lumped components. The design technique based on cascading overall circuit into blocks and computer-aided design of electrical circuit is presented. Experimental measurements were compared with modeling. The insertion losses in the passband (100 MHz) were less than 2 dB and the attenuation more than 20 dB in the stopband. The area occupied by the filter is 6.6/spl times/6.6/spl times/0.836 mm/sup 3/ in plane.     

Design of IIR digital filters in the complex domain by transforming the desired response

In this paper, we present a new design method of infinite impulse response (IIR) digital filters with quasi-equiripple absolute error in the complex domain. This method is based on solving a least squares solution iteratively. At each iteration, the desired response for the least squares approximation is transformed to have equiripple error. This algorithm is efficient because there is no need for any initial value or complex optimization algorithm. By this method, a quasi-equiripple solution is obtained very quickly with less computational complexity. Moreover, by multiplying an arbitrary weighting function on the desired responses of passband and stopband, respectively, the error at the passband and stopband can be controlled. Finally, we show some examples to validate the proposed method.     

Interleave filter based on coherent optical transversal filter

The principle of the transversal interleave filter previously proposed as a novel class of interleave filter is described. The principle of a conventional 1 /spl times/ 1 coherent optical transversal filter is reviewed. Then, the fundamental operating principle and the three design conditions required for the novel interleave filter are explained. As examples, three types of filter design, namely 1) a general/transposed design; 2) an asymmetric design; and 3) a symmetric design, are presented, and their interleave filter characteristics are discussed. The designed interleave filters with a free spectral range of 100 GHz was fabricated using silica-based planar lightwave circuit (PLC) technology. The asymmetric design achieved a wide 3-dB passband width of 55 GHz, whereas an ordinary lattice-form interleave filter could not realize a 3-dB passband width larger than 50 GHz because of the halfband property. A small polarization-dependent wavelength shift of 0.01 nm is demonstrated by inserting a single half waveplate in the middle of the circuit. The general/transposed and symmetric designs realized a practical interleave filter with a boxlike transmission spectrum and low chromatic dispersion. The two-stage interleave filter formed by cascading the general and transposed designs has the advantages of a low crosstalk of less than -46 dB and a wide 20-dB stopband width of 40 GHz, whereas the single-stage symmetric design has an extremely small chromatic dispersion of within /spl plusmn/5 ps/nm. In addition, the design concept to realize a 1/spl times/N transversal interleave filter is extended.     

B-spline design of maximally flat and prolate spheroidal-type FIRfilters

A digital FIR filter is described that offers excellent passband and stopband characteristics for general applications. Design formulae include parameters that adjust the magnitude response from one having characteristics like the maximally flat designs of Hermann (1971) and Kaiser (1975, 1979) to one having characteristics like the minimum-sidelobe energy approximations of Kaiser and Saramaki (1989). The impulse response coefficients are more straightforward to obtain than these filter designs while offering preferable response characteristics in many instances. Unlike FIR filters designed by window- or frequency-sampling methods, the filter coefficients are determined from the inverse Fourier transform in closed form once B-splines have been used to replace sharp transition edges of the magnitude response. Although the filters are developed in the frequency domain, a convergence window is identified in the convolution series and compared with windows of popular FIR filters. By means of example, adjustment of the transitional parameter is shown to produce a filter response that rivals the stopband attenuation and transition width of prolate spheroidal designs. The design technique is extended to create additional transitional filters from prototype window functions, such as the transitional Hann window filter. The filters are particularly suitable for precision filtering and reconstruction of sampled physiologic and acoustic signals common to the health sciences but will also be useful in other applications requiring low passband and stopband errors