Design of stable IIR digital filter based on least P-power error criterion

In this paper, the least p-power error criterion is presented to design digital infinite impulse response (IIR) filters to have an arbitrarily prescribed frequency response. First, an iterative quadratic programming (QP) method is used to design a stable unconstrained one-dimensional IIR filter whose optimal filter coefficients are obtained by solving the QP problem in each iteration. Then, the proposed method is extended to design constrained IIR filters and two-dimensional IIR filters with a separable denominator polynomial. Finally, design examples of the low-pass filter are demonstrated to illustrate the effectiveness of the proposed iterative QP method.     

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.     

巴特沃斯数字陷波滤波器的设计

随着数字技术的发展,数字滤波器在许多领域得到广泛的应用。研究一种在Matlab语言环境下设计IIR数字陷波滤波器的方法,在数字陷波滤波器设计过程中,先进行模拟低通滤波器的设计,然后进行模拟低通/模拟带阻滤波器转换,最后采用双线性变化法将模拟陷波滤波器转化成数字陷波滤波器。提出一种用所有零点和极点来表达数字陷波器传递函数的方法,同时给出以巴特沃斯模拟低通为原型设计数字陷波滤波器的程序。     

Adaptive digital notch filter design on the unit circle for theremoval of powerline noise from biomedical signals

Investigates adaptive digital notch filters for the elimination of powerline noise from biomedical signals. Since the distribution of the frequency variation of the powerline noise may or may not be centered at 60 Hz. Three different adaptive digital notch filters are considered. For the first case, an adaptive FIR second-order digital notch filter is designed to track the center frequency variation. For the second case, the zeroes of an adaptive IIR second-order digital notch filter are fixed on the unit circle and the poles are adapted to find an optimum bandwidth to eliminate the noise to a pre-defined attenuation level. In the third case, both the poles and zeroes of the adaptive IIR second-order filter are adapted to track the center frequency variation within an optimum bandwidth. The adaptive process is considerably simplified by designing the notch filters by pole-zero placement on the unit circle using some suggested rules. A constrained least mean-squared algorithm is used for the adaptive process. To evaluate their performance, the three adaptive notch filters are applied to a powerline noise sample and to a noisy EEG as an illustration of a biomedical signal     

Sampled-data IIR filtering via time-mode signal processing

In this work, the design of sampled-data infinite impulse response (IIR) filters based on time-mode signal processing (TMSP) circuits is presented. Time-mode signal processing, defined as the processing of sampled analog information using time-difference variables, is still a relatively new technology, and therefore, there is still much development needed to extend the technology into a general signal-processing tool. In this work, a set of general building blocks will be introduced that perform the most basic mathematical operations in the time-mode. By arranging these basic structures, higher-order time-mode systems, specifically, time-mode IIR filters, will be realized. A second low-pass time-mode IIR filter is implemented using discrete components. Measured results confirmed that the circuit performed low-pass filtering, providing a maximum SNR of 45.2?dB and SNDR of 35.3?dB.     

用双线性变换法设计IIR滤波器

给出了用双线性变换法设计IIR数字滤波器的方法,并通过用MATLAB语言来实现。双线性法可以使系统经变换后仍保持原有特性,而且这种方法是S域和Z域的单值一一对应,克服了频率交叠产生的混叠效应;最后使用MATLAB语言实现了满足要求的低通IIR滤波器,从而证明了椭圆滤波器具有最优特性。     

A mixed-signal approach for tuning continuous-time low-pass filters

A mixed-signal approach for tuning the bandwidth of continuous-time low-pass filters is presented. The tuning loop uses common circuit blocks (a data converter and digital filters). Simulation results are presented for a number of filters, and measured results are presented for tuning second-order and fourth-order filters.     

Novel single-stage second-order structure for low-pass wide-band low-power continuous-time filters

A novel single-stage second-order structure for Gm-C filters is presented. It allows ample reduction in hardware and thus power consumption. Moreover, due to exploiting otherwise parasitic poles, the structure allows much higher bandwidth than in conventional designs, be achieved. To verify effectiveness of new concept, and based on the new approach to implement second-order stages, a third-order and a fifth-order continuous-time low-pass filters were implemented. The filters fabricated in a CMOS process, achieved more than 430 MHz, bandwidth and less than THD for a 400 mV_p–p 100 MHz input signal. All these accomplished with a factor of about four reduction in hardware and power. The bandwidth, output voltage swing, and dynamic range are far larger than those of any other CMOS low-pass filters thus far reported, which have bandwidth higher than 100 MHz.     

A digital filter approach for complex frequency-shifted perfectly matched layer in semivectorial FDTD

A new formulation of the perfectly matched layer (PML) for the semivectorial finite-difference time-domain (FDTD) method in optical waveguide simulation is presented by incorporating the infinite-impulse response (IIR) digital filter technique. The complex frequency-shifted PML is implemented through Z transformation, where the second-order derivatives in semivectorial FDTD are realized by two cascaded first-order recursive IIR digital filters. The numerical examples indicate that the new scheme has better performance compared with the normal PML.     

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.     

Recursive weighted median filters admitting negative weights andtheir optimization

A recursive weighted median (RWM) filter structure admitting negative weights is introduced. Much like the sample median is analogous to the sample mean, the proposed class of RWM filters is analogous to the class of infinite impulse response (IIR) linear filters. RWM filters provide advantages over linear IIR filters, offering near perfect “stopband” characteristics and robustness against noise. Unlike linear IIR filters, RWM filters are always stable under the bounded-input bounded-output criterion, regardless of the values taken by the feedback filter weights. RWM filters also offer a number of advantages over their nonrecursive counterparts, including a significant reduction in computational complexity, increased robustness to noise, and the ability to model “resonant” or vibratory behavior. A novel “recursive decoupling” adaptive optimization algorithm for the design of this class of recursive WM filters is also introduced. Several properties of RWM filters are presented, and a number of simulations are included to illustrate the advantages of RWM filters over their nonrecursive counterparts and IIR linear filters     

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     

Design of Two-Dimensional Adaptive Digital Notch Filters

In this paper, a method for realizing a two-dimensional (2-D) adaptive notch filter is proposed. The obtained 2-D structure contains a pair of one-dimensional (1-D) second-order IIR notch filters and a pair of 1-D first-order allpass filters. The method has been successfully applied for the removal of a sinusoidal interference superimposed on an image.     

New conversion methods for realizing nonminimum phase transfer functions

New methods are described for converting second-order active-RC low-pass, high-pass, and bandpass filters to obtain nonminimum phase-transfer characteristics. Some of the realizations obtained are superior to other realizations arrived at using well-known conversion methods. Design equations for each realization are summarized in a table. Experimental results are included.     

Intelligent learning algorithms for adaptive digital filters

It is wellknown that gradient search fails in adaptive IIR filters, since their mean-square error surfaces may be multi-modal. In the letter a new approach based on learning algorithms is shown to be capable of performing global optimisation. The new algorithms are suitable for both adaptive FIR and IIR filters.<>     

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     

A real-time programmable switched-capacitor filter

Four independent real-time programmable switched-capacitor filters have been fabricated on a single NMOS chip. The filters are second-order sections with digitally programmable Q and center frequency. Either low-pass or bandpass functions are available by selecting the appropriate input. The device is microprocessor compatible and includes permanent programming capability as well as an on-chip oscillator. The circuit implementation, programming capability, and operation are described.     

Statistical Performance of the Memoryless Nonlinear Gradient Algorithm for the Constrained Adaptive IIR Notch Filter

Gradient-type algorithms for the adaptive infinite-impulse response (IIR) notch filters are very attractive in terms of both performance and computational requirements for various real-life applications. This paper presents, in detail, a statistical analysis of the memoryless nonlinear gradient (MNG) algorithm applied to the well-known second-order adaptive IIR notch filter with constrained poles and zeros. This analysis is based on a proper use of Taylor series expansion and nonlinearization of output signals of the notch and gradient filters. Two difference equations are derived first for the convergence in the mean and mean square senses, respectively. Two closed-form expressions, one for the steady-state estimation bias and the other for the mean-square error, are then derived based on the difference equations, with the former valid for both fast and slow adaptations and the latter valid for slow adaptation only. A closed-form coarse stability bound for the step size parameter of the algorithm is also derived. Extensive simulations are performed to reveal the validity and limitations of the analytical findings. Comparisons between the MNG and the conventional plain gradient algorithm are also made.