A fast algorithm for designing stack filters

Stack filters are a class of nonlinear filters with excellent properties for signal restoration. Unfortunately, present algorithms for designing stack filters can only be used for small window sizes because of either their computational overhead or their serial nature. This paper presents a new adaptive algorithm for determining a stack filter that minimizes the mean absolute error criterion. The new algorithm retains the iterative nature of many current adaptive stack filtering algorithms, but significantly reduces the number of iterations required to converge to an optimal filter. This algorithm is faster than all currently available stack filter design algorithms, is simple to implement, and is shown in this paper to always converge to an optimal stack filter. Extensive comparisons between this new algorithm and all existing algorithms are provided. The comparisons are based both on the performance of the resulting filters and upon the time and space complexity of the algorithms. They demonstrate that the new algorithm has three advantages: it is faster than all other available algorithms; it can be used on standard workstations (SPARC 5 with 48 MB) to design filters with windows containing 20 or more points; and, its highly parallel structure allows very fast implementations on parallel machines. This new algorithm allows cascades of stack filters to be designed; stack filters with windows containing 72 points have been designed in a matter of minutes under this new approach.     

A training framework for stack and Boolean filtering-fast optimaldesign procedures and robustness case study

A training framework is developed in this paper to design optimal nonlinear filters for various signal and image processing tasks. The targeted families of nonlinear filters are the Boolean filters and stack filters. The main merit of this framework at the implementation level is perhaps the absence of constraining models, making it nearly universal in terms of application areas. We develop fast procedures to design optimal or close to optimal filters, based on some representative training set. Furthermore, the training framework shows explicitly the essential part of the initial specification and how it affects the resulting optimal solution. Symmetry constraints are imposed on the data and, consequently, on the resulting optimal solutions for improved performance and ease of implementation. The case study is dedicated to natural images. The properties of optimal Boolean and stack filters, when the desired signal in the training set is the image of a natural scene, are analyzed. Specifically, the effect of changing the desired signal (using various natural images) and the characteristics of the noise (the probability distribution function, the mean, and the variance) is analyzed. Elaborate experimental conditions were selected to investigate the robustness of the optimal solutions using a sensitivity measure computed on data sets. A remarkably low sensitivity and, consequently, a good generalization power of Boolean and stack filters are revealed. Boolean-based filters are thus shown to be not only suitable for image restoration but also robust, making it possible to build libraries of "optimal" filters, which are suitable for a set of applications.     

Modeling of penalties on chains of optical amplifiers withequalizing filters

A mathematical model for the calculation of optical signal-to-noise ratio (SNR) on cascades of erbium doped fiber amplifiers (EDFA's) with interposed equalizing filters in the fiber spans is presented. The model enables to simulate different types of cascade, whether the filters are placed after each amplifier or after any group of amplifiers. Criteria for the design of the optimal filter are presented for a typical configuration. The relation between preemphasis and penalty on SNR is studied, and for the first time to our knowledge it is shown that some asymmetry may arise when using in line optical filters. A study of the sensitivity of penalty at receiver toward preemphasis at transmitter based on the model is presented     

Design and Multiplierless Realization of Digital Synthesis Filters for Hybrid-Filter-Bank A/D Converters

This paper studies the optimal least squares and minimax design and realization of digital synthesis filters for hybrid-filter-bank analog-to-digital converters (HFB ADCs) to meet a given spurious-free dynamic range (SFDR). The problem for designing finite-impulse-response synthesis filters is formulated as a second-order cone-programming problem, which is convex and allows linear and quadratic constraints such as peak aliasing error to be incorporated. The fixed coefficients of the designed synthesis filters are efficiently implemented using sum-of-power-of-two (SOPOT) coefficients, while the internal word length used for each intermediate data is minimized using geometric programming. The main sources of error are analyzed, and a new formula of SFDR in terms of these errors is derived. The effects of component variations of analog analysis filters on the HFB ADC are also addressed by means of two new robust HFB ADC design algorithms based on stochastic uncertainty and worst case uncertainty models. Design results show that the proposed approach offers more flexibility and better performance than conventional methods in achieving a given SFDR and that the robust design algorithms are more robust to parameter uncertainties than the nominal design in which the uncertainties are not taken into account.     

Two improved nyquist filters with piece-wise rectangular-polynomial frequency characteristics

In this article a novel method for constructing a family of improved Nyquist filters is provided, as well as some guidelines on how the inter-symbol interference (ISI) problem can be approached. The proposed solution for the design of Nyquist pulses is based on a piece-wise rectangular-polynomial frequency characteristic using second and third degree polynomials. The characteristic property of the novel family of ISI-free pulses generated by the proposed filters is the asymptotic decay rate of t⁻². By introducing this approach, comparable or better results are obtained in terms ISI performance as compared to several recently proposed pulses.     

Improving the testability of switched-capacitor filters

A design-for-test methodology for SC filters is presented, based on an architecture using some additional circuitry and providing extra capabilities for both off- and on-line tests. The approach uses a comparison (voting) mechanism to indicate whether or not two copies of a filter element (a biquad, for instance) have a similar response during their actual operation. The design and implementation of a few filter examples are included to assess the potential usefulness of this new approach.     

Improving the testability of switched-capacitor filters

A design-for-test methodology for SC filters is presented, based on an architecture using some additional circuitry and providing extra capabilities for both off-and on-line tests. The approach uses a comparison (voting) mechanism to indicate whether or not two copies of a filter element (a biquad, for instance) have a similar response during their actual operation. The design and implementation of a few filter examples are included to assess the potential usefulness of this new approach.     

Bayesian techniques for known channel deconvolution

This paper introduces a new family of deconvolution filters for digital communications subject to severe intersymbol interference. These fixed lag smoothing filters for known channel demodulation are called Bayesian filters. Bayesian filters are derived using a new approach to suboptimal recursive minimum mean square error estimation for non-Gaussian processes. The family of Bayesian filters interpolates between the optimum fixed lag linear filter (i.e., the Kalman filter) and the optimum fixed lag symbol-by-symbol demodulator in both performance and complexity. The complexity of the Bayesian filter is exponential in a parameter, typically chosen smaller than the channel length and the filter lag. Hence, the Bayesian filter decouples the channel length and the filter lag from the exponential complexity in these parameters found in many other high performance demodulation algorithms. Simulations characterize the performance and compare the Bayesian filter to both optimal and reduced complexity demodulation algorithms     

Theory and design of signal-adapted FIR paraunitary filter banks

We study the design of signal-adapted FIR paraunitary filter banks, using energy compaction as the adaptation criterion. We present some important properties that globally optimal solutions to this optimization problem satisfy. In particular, we show that the optimal filters in the first channel of the filter bank are spectral factors of the solution to a linear semi-infinite programming (SIP) problem. The remaining filters are related to the first through a matrix eigenvector decomposition. We discuss uniqueness and sensitivity issues. The SIP problem is solved using a discretization method and a standard simplex algorithm. We also show how regularity constraints may be incorporated into the design problem to obtain globally optimal (in the energy compaction sense) filter banks with specified regularity. We also consider a problem in which the polyphase matrix implementation of the filter bank is constrained to be DCT based. Such constraints may also be incorporated into our optimization algorithm; therefore, we are able to obtain globally optimal filter banks subject to regularity and/or computational complexity constraints. Numerous experiments are presented to illustrate the main features that distinguish adapted and nonadapted filters, as well as the effects of the various constraints. The conjecture that energy compaction and coding gain optimization are equivalent design criteria is shown not to hold for FIR filter banks     

Equivariant holomorphic filters for contour denoising and rapid object detection.

It is well known that linear filters are not powerful enough for many low-level image processing tasks. However, it is also very difficult to design robust nonlinear filters that respond exclusively to features of interest and that are, at the same time, equivariant with respect to translation and rotation. This paper proposes a new class of rotation-equivariant nonlinear filters that is based on the principle of group integration. These filters become efficiently computable by an iterative scheme based on repeated differentiation of products and summations of intermediate results. The relations of the proposed approach to Volterra filters and steerable filters are shown. In the context of detection problems, the filter may be interpreted as some kind of generalized Hough transform. The experiments show that the new filter can be used for enhancing noisy contours and rapid object detection in microscopical images. In the detection context, our experiments show that the proposed filter is definitely superior to alternative approaches, when high localization accuracy is required.     

Mildly suboptimal digital filters using a host windowing approach

A digital-filter design technique is described which employs simple trigonometric windowing of a `host? digital filter. In contrast to the usual windowing rationale which uses a truncated ideal impulse response, this approach uses an optimal (finite-length-minimax) host impulse response. It is shown that optimal Hilbert-transform filters serve as suitable hosts for lowpass filters of even-length impulse response, and optimal differentiators can be used as hosts for odd-length impulse responses. The resulting windowed filters are no longer optimal, but yield approximation errors under most operating conditions.     

An L1-Method for the Design of Linear-Phase FIR Digital Filters

This paper considers the design of linear-phase finite impulse response digital filters using an L₁ optimality criterion. The motivation for using such filters as well as a mathematical framework for their design is introduced. It is shown that L₁ filters possess flat passbands and stopbands while keeping the transition band comparable to that of least-squares filters. The uniqueness of L₁-based filters is explored, and an alternation type theorem for the optimal frequency response is derived. An efficient algorithm for calculating the optimal filter coefficients is proposed, which may be viewed as the analogue of the celebrated Remez exchange method. A comparison with other design techniques is made, demonstrating that the L₁ approach may be a good alternative in several applications.     

Design of multiplierless fir filters by multiple use of the same filter

A novel approach to the design of multiplierless filters, based on the ACF (amplitude change function), is discussed. The prototype filter chosen is a CCOS (the cascade of the cosine functions) which requires no multipliers and only some adders. The required filter specifications are met by multiple use of the same CCOS filter. Effects due to coefficient quantisation do not arise when using the new approach. No multipliers are required to implement this filter.<>     

A step-by-step active-filter design

This article presents, in a simplified manner, a design method for active filters intended for those who are not filter specialists. By following the described five-step approach, a circuit designer who has some knowledge of passive filters will (without having to learn a whole new technology) be able to design active filters just as easily as he now handles conventional passive filters. Starting with the filter specification, it is shown sequentially how to realize a network that meets the prescribed requirements. Configurations and element values are given for the low-pass (LP), bandpass (BP), high-pass (HP), all-pass (AP), and band-elimination (BE), second-order active filter building blocks.     

Tracking in Wireless Sensor Networks Using Particle Filtering: Physical Layer Considerations

In this paper, a new framework for target tracking in a wireless sensor network using particle filters is proposed. Under this framework, the imperfect nature of the wireless communication channels between sensors and the fusion center along with some physical layer design parameters of the network are incorporated in the tracking algorithm based on particle filters. We call this approach ldquochannel-aware particle filtering.rdquo Channel-aware particle filtering schemes are derived for different wireless channel models and receiver architectures. Furthermore, we derive the posterior Cramer-Rao lower bounds (PCRLBs) for our proposed channel-aware particle filters. Simulation results are presented to demonstrate that the tracking performance of the channel-aware particle filters can reach their theoretical performance bounds even with relatively small number of sensors and they have superior performance compared to channel-unaware particle filters.     

Design of FIR digital filters with prescribed flatness and peak error constraints using second-order cone programming

This paper studies the design of digital finite impulse response (FIR) filters with prescribed flatness and peak design error constraints using second-order cone programming (SOCP). SOCP is a powerful convex optimization method, where linear and convex quadratic inequality constraints can readily be incorporated. It is utilized in this study for the optimal minimax and least squares design of linear-phase and low-delay (LD) FIR filters with prescribed magnitude flatness and peak design error. The proposed approach offers more flexibility than traditional maximally-flat approach for the tradeoff between the approximation error and the degree of design freedom. Using these results, new LD specialized filters such as digital differentiators, Hilbert Transformers, Mth band filters and variable digital filters with prescribed magnitude flatness constraints can also be derived.     

Optimal weighted median filtering under structural constraints

A new expression for the output moments of weighted median filtered data is derived. The noise attenuation capability of a weighted median filter can now be assessed using the L-vector and M-vector parameters in the new expression. The second major contribution of the paper is the development of a new optimality theory for weighted median filters. This theory is based on the new expression for the output moments, and combines the noise attenuation and some structural constraints on the filter's behavior. In certain special cases, the optimal weighted median filter can be obtained by merely solving a set of linear inequalities. This leads in some cases to closed form solutions for optimal weighted median filters. Some applications of the theory developed in this paper, in 1-D signal processing and image processing are discussed. Throughout the analysis, some striking similarities are pointed out between linear FIR filters and weighted median filters     

形态滤波器结构元的自适应优化算法

该文提出了一种实现形态滤波器结构元优化设计的自适应算法,自适应过程类似于经典的最小均方(LMS)算法。通过将腐蚀与膨胀运算用隐函数表示,推导出腐蚀与膨胀运算中结构元的优化公式,由此进一步可得到任意组合形态滤波器的自适应优化公式。仿真实验表明该算法改善了形态滤波器的性能,具有设计简便、实用性强的特点。     

Design of linear phase M-channel perfect reconstruction FIR filterbanks

We propose two approaches to design M channel nonparaunitary filter banks that satisfy perfect reconstruction (PR) and linear phase (LP) properties. In the first approach, the PR condition is imposed on only a high-pass filter. Although this method does not require nonlinear optimization, it has a demerit in that the order of a high-pass filter becomes high. In the second approach, two filters are optimized simultaneously using a Lagrange-Newton method. We can design PR filter banks that have the same length. The PR constraint is also formulated as a linear and nonlinear equation of the analysis filter coefficients. Finally, some design examples are included     

A Direct Synthesis Approach for Microwave Filters With a Complex Load and Its Application to Direct Diplexer Design

This paper presents a direct synthesis approach for general Chebyshev filters terminated with a complex load. The new approach is based on the fact that the polynomial functions for synthesizing the filters are composed for any matched loads. By normalizing the polynomial functions with assumed complex matched load impedance by a real reference load impedance using power waves normalization, a set of new polynomial functions for the same filter, but with real load impedance, can be formulated, from which the coupling matrix for the physical filter design can be obtained using a standard direct filter synthesis approach. This new direct synthesis approach can find many applications. A practical application is the direct diplexer design with a realistic junction model being taken into account. With the diplexer design is concerned, a fast-converged iterative scheme is proposed. The effectiveness and the validation of the proposed scheme are demonstrated by two design examples