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We present a particle-based nonlinear filtering scheme, related to recent work on chainless Monte Carlo, designed to focus particle paths sharply so that fewer particles are required. The main features of the scheme are a representation of each new probability density function by means of a set of functions of Gaussian variables (a distinct function for each particle and step) and a resampling based on normalization factors and Jacobians. The construction is demonstrated on a standard, ill-conditioned test problem. pseu-Gaussian | Jacobian | chainless sampling doi/ 10.1073/pnas.0909196106

Orthogonal frequency-division multiplexing (OFDM) can be used to support high-data-rate transmissions over time-dispersive fading channels. Many OFDM-based communication systems use packet-based transmission, where channel estimation is needed for the detection of information-carrying symbols. The finite impulse response (FIR) channel model is simple and effective for some simulations of channel estimation for the OFDM-based communication systems over the time-dispersive channels; yet, it is only an approximate channel model that cannot be used in the case of accurate channel estimation. Unfortunately, many researchers have overlooked this issue and have been devising channel-estimation algorithms squarely based on the FIR channel model. While the channel estimation results from these algorithms can be impressive for the FIR channels, the algorithms can hardly be applied in real-world applications. This paper explains in detail the reason the FIR channel model is only an approximate channel model for the OFDM-based communication systems, trying to discourage the inappropriate usage of this model, which can lead to fruitless efforts. This paper also presents a realistic channel model for OFDM-based communication systems, which can be used to realistically access the channel parameter-estimation algorithms. Index Terms--Channel estimation, channel model, orthogonal frequency-division multiplexing (OFDM).

In this paper, we present incremental smoothing and mapping (iSAM), which is a novel approach to the simultaneous localization and mapping problem that is based on fast incremental matrix factorization, iSAM provides an efficient and exact solution by updating a QR factorization of the naturally sparse smoothing information matrix, thereby recalculating only those matrix entries that actually change, iSAM is efficient even for robot trajectories with many loops as it avoids unnecessary fill-in in the factor matrix by periodic variable reordering. Also, to enable data association in real time, we provide efficient algorithms to access the estimation uncertainties of interest based on the factored information matrix. We systematically evaluate the different components of iSAM as well as the overall algorithm using various simulated and real-world datasets for both landmark and pose-only settings. Index Terms--Data association, localization, mapping, mobile robots, nonlinear estimation, simultaneous localization and mapping (SLAM), smoothing.

Multimedia communications require efficient and real-time implementations of multirate digital signal processing systems. The backbone structures of multirate systems are digital multirate filter banks. Therefore, efficient multimedia communications rely, in the first place, on real-time implementations of multirate filter banks. In this paper, we describe a Field Programmable Gate Array (FPGA) implementation of the analysis and synthesis filter banks which are the fundamental components of multirate systems. The implementation utilizes the parallel form of the distributed arithmetic technique which enables maximum exploitation of the parallelism inherent in the multirate filtering operation. Performance results demonstrate the effectiveness of the implementation and suggest that the FPGA platform is indeed attractive for implementing multirate filter banks.. Key words: Multirate Filter Banks, Filed Programmable Gate Arrays (FPGAs), xilinx virtex devices, parallel distributed arithmetic, efficient parallel implementation, INTRODUCTION Multimedia digital signal processing applications require sampling audio and video signals using different sampling rates (1). This requirement has given rise to the design, development and application of multirate [...]

This technical note proposes a novel output-feedback control law based on a finite impulse response (FIR)-type quasi-deadbeat observer for linear systems. For nominal systems without disturbances, this technical note first establishes the deadbeat condition that reduces the state estimation error to zero within a finite time and verifies that all the hidden poles of the closed-loop system under the quasi-deadbeat observer-based control law are zero and that the separation principle holds true. In order to enhance the disturbance rejection capability for systems with random-work disturbances, on the structural merit of the FIR-type observer, we have proposed the conditions for an [H.sub.[infinity]] quasi-deadbeat observer and an [H.sub.[infinity]] stabilizer based on the predetermined observer, respectively. Index Terms--Deadbeat property, finite impulse response (FIR) structure, separation principle, [H.sub.[infinity]] performance.

We discuss and implement a log-polar transform-based distortion-invariant filter for automatic target recognition applications. The log-polar transform is a known space-invariant image representation used in several image vision systems to eliminate the effects of scale and rotation in an image. For in-plane rotation invariance and scale invariance, a log-polar transform-based filter was synthesized. In cases of in-plane rotation invariance, peaks shift horizontally, and in cases of scale invariance, peaks shift vertically. To achieve out-of-plane rotation invariance, log-polar images were used to train the wavelet-modified maximum average correlation height (WaveMACH) filter. The designed filters were implemented in the hybrid digital-optical correlation scheme. It was observed that, for a certain range of rotation and scale differences, the correlation signals merge with the strong dc. To solve this problem a shift was introduced in the log-polar image of the target. The use of a chirp function for dc removal has also been discussed. Correlation peak height and peak-to-sidelobe ratio have been calculated as metrics of goodness of the log-polar transform-based WaveMACH filter. Experimental results are presented. OCIS codes: 070.0070, 070.4550, 070.5010, 100.3008.

In this brief, a procedure for digital filters design is presented. The main purpose is to show that a digital filter and its realization can be simultaneously determined such as to minimize an upper bound of the [H.sub.2] norm of the estimation error and impose a certain degree of robustness against practical uncertainties as for instance, finite word length implementation, roundoff errors, and numerical precision. The optimal filter and its state-space realization are jointly determined from the solution of a convex programming problem expressed in terms of linear matrix inequalities. A simple illustrative example is presented for comparison purposes making clear the advantages of the reported results. Index Terms--Digital filters, Kalman filters, optimization, robustness.

The finite horizon [H.sub.[infinity]] fixed-lag smoothing problem for linear descriptor systems is considered and a sufficient condition for the existence of an [H.sub.[infinity]] smoother is derived. The key approach applied for deriving the [H.sub.[infinity]] fixed-lag smoother is the reorganization innovation analysis in Krein space. Under the Krein space, the [H.sub.[infinity]] fixed-lag smoothing is converted into an [H.sub.2] estimation problem for the system with current and delayed measurements. By using innovation re-organization approach, we show that the [H.sub.2] estimation with delayed measurements is transformed into a problem of delay-free measurements and thus a simple solution to [H.sub.[infinity]] smoothing is given. At last, an illustrative example shows the efficiency of the proposed estimator. Index Terms--Descriptor systems, innovation analysis, fixed-lag smoothing, [H.sub.[infinity]] estimation.

In this brief, we present a digit-reconfigurable finite-impulse response (FIR) filter architecture with a very fine granularity. It provides a flexible yet compact and low-power solution to FIR filters with a wide range of precision and tap length. Based on the proposed architecture, an 8-digit reconfigurable FIR filter chip is implemented in a single-poly quadruple-metal 0.35-[micro]m CMOS technology. Measurement results show that the fabricated chip operates up to 86 MHz when the filter draws 16.5 mW of power from a 2.5-V power supply. Index Terms--Canonical signed digit (CSD), finite-impulse response (FIR) digital filters, reconfigurable architectures.

In this paper, a digital fractional-order differentiator (FOD) is designed by using fractional sample delay. To improve the design accuracy of conventional fractional differencing and Tustin design methods at high frequency regions, the integer delay is replaced by fractional sample delay. By using the well-documented finite-impulse-response Lagrange, infinite impulse response allpass, and Farrow fractional delay filters, the proposed FOD can be implemented easily even though the fractional sample delay is introduced. Several design examples are illustrated to demonstrate the effectiveness of the proposed method. Index Terms--Allpass filter, finite-impulse-response (FIR) filter, fractional differencing, fractional-order differentiator (FOD), fractional sample delay, infinite-impulse-response (IIR) filter.

This paper presents the development and test of some of the electronic boards that have been designed for the upgrade of the L1 calorimeter trigger at the D0 experiment. The analog to digital converter and filter board (ADF) digitizes 32 calorimeter channels, applies digital filtering, and sends data to the next processing stage via 2 Gb/s links. The board is designed for sustained operation at 7.57 MHz with an end-to-end latency of less than ~1 [micro]s. In order to test the high-speed output links of the ADF board, we made a tester that comprises a custom made Channel Link receiver card. To connect a prototype ADF board to the D0 detector without disturbing the existing trigger system, we designed a splitter board that duplicates the analog signals from eight calorimeter channels. The serial command link distribution card (SCLD) is designed to accurately distribute synchronization signals to the 80 ADF boards of the final system. We made single channel versions of the ADF and SCLD boards. These cards run in a simple desktop PC environment and are helpful for tests and collaborative work. We describe the hardware, firmware and software aspects of the various developments and show the operation of the different boards. We present performance measurements made on the prototype ADF board, and explain how we defined the production model of this board. Index Terms--Digital filters, high speed links, timing distribution circuits, trigger.

In this paper, a new algorithm, called contention resolution algorithm for weight-two subexpressions (CRA-2), based on an ingenious graph synthesis approach has been developed for the common subexpression elimination of the multiplication block of digital filter structures. CRA-2 provides a leeway to break away from the local minimum and the flexibility of varying optimization options through a new admissibility graph. It manages two-bit common subexpressions and aims at achieving the minimal logic depth as the primary goal. The performances of our proposed algorithm are analyzed and evaluated based on benchmarked finite-impulse-response filters and randomly generated data. It is demonstrated that CRA-2 achieves the shortest logic depth with significant reduction in the number of logic operators compared with other reported algorithms. Index Terms--Common subexpression elimination (CSE), logic depth, multiple constants multiplication.

The problem of minimizing an [L.sub.2]-sensitivity measure subject to [L.sub.2]-norm dynamic-range scaling constraints for state-space digital filters is formulated. It is shown that the problem can be converted into an unconstrained optimization problem by using linear-algebraic techniques. Next, the unconstrained optimization problem is solved by applying an efficient quasi-Newton algorithm with closed-form formula for gradient evaluation. The coordinate transformation matrix obtained is then used to construct the optimal state-space filter structure that minimizes the [L.sub.2]-sensitivity measure subject to the scaling constraints. A numerical example is presented to illustrate the utility of the proposed technique. Index Terms--[L.sub.2]-norm dynamic-range scaling constraints, [L.sub.2]-sensitivity, optimal realization, scaling-constrained sensitivity minimization, state-space digital filters.

We present the experimental application and comparison of two methods for the synthesis of digital filters, which represent the state-of-the-art of optimum digital processing of shaped signals with arbitrary constraints in time and frequency domain, and any kind of stationary noise power spectral density. The methods are implemented in experimental measurement setups, and optimum filters are synthesized with regard to assigned constraints (e.g., finite duration, flat top, peaking time, zero area, etc.) and by taking into account the real environmental noise or disturbance present in the system, identified from datasets of simple signal experimental acquisitions. Implementation issues are detailed and basic design rules for digital signal processors based on these techniques are derived. Index Terms--DSP, energy resolution, high-resolution spectroscopy, HPGe detectors, LMS data analysis, optimum digital spectroscopy.

This brief studies the design of complex-valued variable digital filters (CVDFs) and their applications to the efficient arbitrary sample rate conversion for complex signals. The design of CVDFs using either the minimax or least-squares criteria is formulated as a convex optimization problem and solved using the second-order cone programming (SOCP). In addition, linear and convex quadratic inequality constraints can be readily incorporated. Design examples are given to demonstrate the effectiveness of the proposed approach. Index Terms--Complex-valued variable digital filter (CVDF) design, flatness and peak error constraints, low delay, sampling rate conversion, second-order cone programming (SOCP).

A simple method is given for deriving the spectral transformations for infinite-impulse response (IIR) filters, which can be used to transform a prototype low-pass (LP) digital filter to another LP, high-pass (HP), bandpass (BP), or band-stop (BS) digital filter with prescribed passband edge(s) and the same tolerances as those of the prototype. The method is based on a combination of bilinear transformation with the analog frequency transformation and is simpler--conceptually, as well as from the calculation point of view--than the conventional method based on all-pass transformation functions. Index Terms--Digital filters, digital signal processing, infinite-impulse response (IIR) filters, spectral transformation.

Singular-value decomposition (SVD) can be efficiently utilized to obtain the optimal vector-array decomposition (VAD) for simplifying real-coefficient variable digital filter design problem, but the SVD-based VAD methods are not applicable to the design of complex-coefficient variable filters. This paper proposes a successive algorithm for decomposing arbitrary multidimensional complex array into the VAD form, and thus, a complex-coefficient variable digital filter with arbitrary variable frequency response can be easily obtained through constant complex-coefficient filter design and multidimensional polynomial fitting. The new VAD algorithm successively decomposes the complex array and its residual arrays into the vector-array pairs stage by stage, and each stage contains an iterative optimization that can be easily solved in a closed-form. Our computer simulations have demonstrated that the successive VAD converges very fast to the optimal solution. Index Terms--Complex-coefficient filter, constant digital filter, real-coefficient filter, singular-value decomposition (SVD), variable digital filter, vector-array decomposition (VAD).

We propose and demonstrate the application of concepts from digital filter design in order to optimize artificial optical resonant structures to produce a nearly ideal nonlinear phase shift response. Multistage autoregressive moving average (ARMA) optical filters (ring-resonator-based Math-Zehnder interferometer lattices) are designed and studied. The filter group delay is used as a measure instead of finesse or quality factor to study the nonlinear sensitivity for multiple resonances. The nonlinearity of a four-stage ARMA filter is 17 times higher than that of the intrinsic material of the same group delay. We demonstrate that the nonlinear sensitivity can be increased within constant bandwidth by allocating more in-band phase or by using higher-order filter structures and that the nonlinear sensitivity enhancement improves with increasing group delay. We also investigate methods to precompensate the nonlinear response to reduce the occurrence of optical bistabilities. The effect of optical loss, including linear absorption and two-photon absorption, is discussed in postanalysis. In addition, we discuss how the improvement in nonlinear response scales with respect to various filter parameters. OCIS codes: 190.0190, 190.3270, 230.5750, 120.2440.

The problem of designing efficient detection techniques for multicarrier transmission systems operating in the presence of narrowband interference (NBI) is addressed. New widely linear (WL) zero-forcing (ZF) receivers for multicarrier systems are synthesized, which mitigate the NBI contribution at the receiver output, without requiring knowledge of the NBI statistics.

A novel scheme for identifying the impulse response of a sparse channel is presented. The main advantage of this scheme is that two short adaptive filters can be used instead of one long adaptive filter resulting in faster overall convergence and reduced computational complexity and storage.

An entropy-directed deterministic annealing optimization algorithm is presented and its applicability to the problem of designing digital filters with discrete coefficients, each implemented as a sum of signed power of two terms and additional general hardware constraints is shown. The algorithm is based on analogies from statistical mechanics and is related to the well-known mean field annealing algorithm.

Most standard wave digital filters are derived from passive reference circuits, where only parallel and serial connections between one-port elements occur. In this paper, a framework for the automated generation of the wave digital structures is presented, where the reference circuit is assumed to comprise arbitrary connection types. It is shown how the representation of the underlying graph by its so-called SPQR-tree is related to a suitable adaptor structure and how this concept can be generalized to also cope with networks containing certain multiport elements. We propose two different novel approaches to finding a valid tree representation from a given reference circuit. The first approach relies on the usage of apt replacement graphs for the multiport elements. The second one is based on searches for circles on suitably constructed graph representations and generates wave digital structures with minimum implementation effort even in presence of nonreciprocal elements. In both approaches, standard separation algorithms with known efficient implementations can be applied. Index Terms--Delay-free loops, graph connectivity, multiport elements, port-wise separation of Kirchhoff networks, wave digital structures.

An algorithm that allows for different memory lengths of the linear and quadratic Volterra kernel while preserving the advantages of fast convolution techniques in the frequency domain for a second-order Volterra filter is presented. The results improved convergence of a second-order partitioned block frequency-domain adaptive Volterra filter (PBFDAVF) compared with time-domain adaptation of the kernel coefficients.

Subband adaptive filters (SAFs) have gained widespread use in important applications such as echo cancellation, system identification, and equalization and are normally constrained to utilize uniform filterbanks. An adaptive algorithm to control the uniform SAF configurations is theoretically derived.

State space structures (SSSs) and wave digital filters (WDFs) are two major paradigms for the realization of digital filters. Both approaches are well established, but there are no proven methods for a mixed design of digital filters consisting of parts which are realized as SSSs and parts realized as WDFs. This contribution shows how to add a wave port to the conventional SS representation. This wave port allows to interconnect SSSs and WDFs without creating delay-free loops. Such interconnections allow to build discrete-time structures by reusing existing designs from both classes of digital filters. Index Terms--State space structures (SSSs), wave digital filters (WDFs).

Two issues for improving the multiwavelet denoising are studied on the basis of multivariate shrinkage. A simple method for designing second order approximation preserving orthogonal prefilter for any multiplicity is suggested.

This paper proposes a straightforward method for designing variable digital filters with arbitrary variable magnitude as well as arbitrary fixed-phase or variable fractional delay (VFD) responses. The basic idea is to avoid the complicated direct design of one-dimensional (1-D) variable digital filters by decomposing the original variable filter design problem into easier subproblems that only require constant 1-D filter designs and multidimensional polynomial approximations. Through constant 1-D filter designs and multidimensional polynomial fits, we can easily obtain a variable digital filter satisfying the given variable design specifications. To decompose the original variable filter design into constant 1-D filter designs and multidimensional polynomial fits, a new multidimensional complex array decomposition called vector array decomposition (VAD) is proposed, which is based on two new theorems using the singular value decomposition (SVD). Once the VAD is obtained, the subproblems can be easily solved. Furthermore, we show that the VAD can also be generalized to the weighted least squares (WLS) case (WLS-VAD) for the WLS variable filter design. Three design examples are given to illustrate that the WLS-VAD and VAD-based techniques are considerably efficient for designing variable digital filters with arbitrary variable magnitude and arbitrary fixed-phase or VFD responses. Index Terms--Constant digital filter, singular-value-decomposition (SVD), variable digital filter, vector-array decomposition (VAD), weighted least squares VAD (WLS-VAD).

The elaborate design of folded finite-impulse response (FIR) filters based on pipelined multiplier arrays is presented in this paper. The design is considered at the bit-level and the internal delays of the pipelined multiplier array are fully exploited in order to reduce hardware complexity. Both direct and transposed FIR filter forms are considered. The carry-save and the carry-propagate multiplier arrays are studied for the filter implementations. Partially folded architectures are also proposed which are implemented by cascading a number of folded FIR filters. The proposed schemes are compared as to the aspect of hardware complexity with a straightforward implementation of a folded FIR filter based on the pipelined Wallace Tree multiplier. The comparison reveals that the proposed schemes require 20%-30% less hardware. Finally, efficient implementation of partially folded FIR filter circuits is presented when constraints in area, power consumption and clock frequency are given. Index Terms--Digital filters, multiplying circuits, systolic arrays.

The celebrated Kalman-Yakubovic-Popov (KYP) lemma establishes the equivalence between a frequency domain inequality (FDI) and a linear matrix inequality, and has played one of the most fundamental roles in systems and control theory. This paper first develops a necessary and sufficient condition for an S-procedure to be lossless, and uses the result to generalize the KYP lemma in two aspects--the frequency range and the class of systems--and to unify various existing versions by a single theorem. In particular, our result covers FDIs in finite frequency intervals for both continuous/discrete-time settings as opposed to the standard infinite frequency range. The class of systems for which FDIs are considered is no longer constrained to be proper, and nonproper transfer functions including polynomials can also be treated. We study implications of this generalization, and develop a proper interface between the basic result and various engineering applications. Specifically, it is shown that our result allows us to solve a certain class of system design problems with multiple specifications on the gain/phase properties in several frequency ranges. The method is illustrated by numerical design examples of digital filters and proportional-integral-derivative controllers. Index Terms--Control design, digital filter, frequency domain inequality, Kalman-Yakubovic-Popov (KYP) lemma, linear matrix inequality (LMI).

A new method for analyzing floating-point roundoff for digital filters is provided using 'finite signal-to-noise' models whose noise sources have variances proportional to the variance or power of the corrupted signals. Findings show that with the new model, a new expression for output error covariance of digital filters is derived when implemented in floating-point digital signal processor using accumulation.

This paper studies the design and multiplier-less realization of a new software radio receiver (SRR) with reduced system delay. It employs low-delay finite-impulse response (FIR) and digital allpass filters to effectively reduce the system delay of the multistage decimators in SRRs. The optimal least-square and minimax designs of these low-delay FIR and allpass-based filters are formulated as a semidefinite programming (SDP) problem, which allows zero magnitude constraint at [omega] = [pi] to be incorporated readily as additional linear matrix inequalities (LMIs). By implementing the sampling rate converter (SRC) using a variable digital filter (VDF) immediately after the integer decimators, the needs for an expensive programmable FIR filter in the traditional SRR is avoided. A new method for the optimal minimax design of this VDF-based SRC using SDP is also proposed and compared with traditional weight least squares method. Other implementation issues including the multiplier-less and digital signal processor (DSP) realizations of the SRR and the generation of the clock signal in the SRC are also studied. Design results show that the system delay and implementation complexities (especially in terms of high-speed variable multipliers) of the proposed architecture are considerably reduced as compared with conventional approaches. Index Terms--Design and multiplier-less realization, low delay, passband linear-phase finite-impulse response (FIR) and allpass filters, sampling rate conversion, semidefinite programming (SDP), software radio receiver (SRR), variable digital filters (VDF).

The paper tries to apply the Butterworth low-pass filter to inertial navigation system (INS) data processing. A set of INS heading data of a practical example has been calculated and the filtering tested. This filtering method is used to examine the correction of the results made by Guo and Wang. Based on the discrete Fourier transformation and the digital filter design technique, a Butterworth low-pass digital filter has been designed and performed to process INS heading raw data. The design of a special Butterworth filter includes determination of the technical specification of the filter and of the response function in the time domain or the frequency domain (determination of the order and cutoff frequency of the digital filter). For the high-frequency noise of INS raw data, a Butterworth low-pass filter has been designed to obtain a more accurate INS heading. The choice of the parameters and orders of the filter is also discussed in the paper. Finally, an example of INS heading data calculation is presented. The signal-processing TOOLBOX of MATLAB software is used for calculating and mapping the results. The result (RMS) is at the level of 0.01[degrees]. The method described here is simpler than Kalman filtering or the smoothing method and has sufficient accuracy for INS processing. It also provides ideas for some other series of raw data with high-frequency noise. CE Database subject headings: Digital filters; Data processing; Noise: Surveys.

A study was conducted to investigate the identifiability conditions for blind and semi-blind finite impulse response (FIR) multichannel estimation, in terms of channel characteristics. The study reveals that the semi-blind methods are superior to blind and training sequence methods, and allow the estimation of any channel with few known symbols.

Digital filters arising in the B-spline signal processing are characterized in a unified manner in this paper. The transfer functions of these filters are the z-transforms of the uniformly sampled central B-splines shifted by an arbitrary value. The transfer functions are cascades of an FIR kernel filter and a simple moving average FIR filter. For certain values of the shift parameter, the filters are identical to those referred to as the B-spline digital filters in the literature. The filters thus form a general family of B-spline digital filters. The kernel part of the B-spline filters may be used for transforming a discrete-time signal to a representation based on the B-spline coefficients. The B-spline filters may also be used to convert a sequence of B-spline coefficients to a discrete-time spline signal. The contributions of the paper are as follows. A unifying recurrence relation enabling the computation of the impulse response coefficients of the B-spline kernel filters is derived. An accompanying recurrence relation is also obtained for the entire transfer function of the kernel filters. The recurrences are valid for arbitrary values of the shift parameter. It is proved that the roots of the transfer functions of the kernel filters are distinct, negative and real. We also prove that the roots of the kernel filters of successive orders interlace. The results regarding the location of the zeros are also valid for arbitrary values of the shift parameter. The relation of the kernel filters to the Eulerain polynomials is discussed. It is shown that for certain choices of the parameters the kernel filters are equivalent to the classical Eulerian polynomials that frequently arise in combinatorics. An alternative closed-form expression for the kernel filters in the Bernstein form is also derived. Besides their importance in unifying the existing results on B-spline filters, the generalized family of B-spline filters studied in this paper find applications in fractional delay of B-spline signals. Index Terms--B-spline interpolation, B-spline signal processing, Bernstein polynomials, digital filters, Eulerain numbers, Eulerain polynomials, finite-impulse response (FIR) filters, fractional delay, recurrence relations, stability.

A new structure for split transversal filtering is proposed and the optimum split Wiener filter is introduced. The approach consists of combining the idea of split filtering with a linearly constrained optimization scheme.

This transactions brief is concerned with designing adaptive filters subject to output envelope constraints in the presence of bounded noise at the input channel. The bound on the noise is used to form the input mask that contains all possible input signals corrupted by noise. The optimal envelope-constrained filter is designed with respect to the entire input mask. A cubic smoothing function is applied to implement the constraint approximation, which paves the way for establishing adaptive algorithms. The adaptive envelope-constrained filter thus designed, achieves guaranteed satisfaction of the output envelope constraints as long as it has converged. Computer simulations that support the theoretical findings are given. Index Terms--Adaptive filtering, bounded noise, channel equalization, envelope constraints, filter design.

In this paper, a second-order RF bandpass filter based on active inductor has been implemented in a 0.35 [micro]m CMOS process. Issues related to the intrinsic quality factor and dynamic range of the CMOS active inductor are addressed. Tuned at 900 MHz with Q = 40, the filter has 28-dB spurious-free-dynamic-range (SFDR) and total current consumption (including buffer stage) is 17 mA with 2.7-V power supply. Experimental results also show the possibility of using them to build higher order RF filter and voltage-controlled oscillator (VCO). Index Terms--Active inductor, Q-enhancement, spurious-free-dynamic-range (SFDR).

This paper presents a synthesis method for infinite-impulse response (IIR) digital filter structures using genetic programming with automatically defined functions (GP-ADF). In the proposed method, digital filter structures are represented as S-expressions with subroutines, which are written directly from the set of difference equations. This paper also shows the condition for the constructing the S-expressions that represent the filter structures without delay-free loops. Numerical examples synthesize two-filter structures: the low-coefficient sensitivity fourth-order filter structure and the low-output roundoff noise second-order filter structure. Index Terms--Digital filter wordlength effects, genetic programming, infinite-impulse response (IIR) digital filters.

An intrinsic M-channel lifting factorization of perfect reconstruction filter banks (PRFBs) is presented as an extension of Sweldens' conventional two-channel lifting scheme. Given a polyphase matrix E(z) of a finite-impulse response (FIR) M-channel PRFB with det(E(z)) = [z.sup.-K], K [member of] Z, a systematic M-channel lifting factorization is derived based on the Monic Euclidean algorithm. The M-channel lifting structure provides an efficient factorization and implementation; examples include optimizing the factorization for the number of lifting steps, delay elements, and dyadic coefficients. Specialization to paraunitary building blocks enables the design of paraunitary filter banks based on lifting. We show how to achieve reversible, possibly multiplierless, implementations under finite precision, through the unit diagonal scaling property of the Monic Euclidean algorithm. Furthermore, filter-bank regularity of a desired order can be imposed on the lifting structure, and PRFBs with a prescribed admissible scaling filter are conveniently parameterized. Index Terms--Cascade algorithm, discrete cosine transform (DCT), greatest common divisor, laurent polynomials, lifting factorization, M-band wavelets, Monic Euclidean algorithm, multiplierless approximations, perfect reconstruction filter banks (PRFBs), regularity, reversible transforms.

An attractive approach to the design of two-dimensional (2-D) digital filters is to decompose the original difficult 2-D design problem into a set of relatively easier subproblems that involve one-dimensional (l-D) filter designs. Lu et al. have shown that the design technique using the singular value decomposition (SVD) can be applied to the design of 2-D filters with arbitrary magnitude and phase responses. The most important point of this paper is to show that some magnitude and phase symmetries can be efficiently exploited in the SVD-based designs, which can reduce the computational complexity and save the computer storage required for 1-D filter (subfilter) coefficients by 50%. Moreover, an objective criterion is proposed for selecting the appropriate subfilter orders in order to reduce the hardware implementation cost. A fractional-delay 2-D filter is designed to illustrate the effectiveness of the SVD-based approach by exploiting the specification symmetries and new order-selecting criterion. Index Terms--Fractional-delay two-dimensional (2-D) filter, magnitude specification symmetry, one-dimensional (1-D) sub-filter, order-selecting criterion, phase specification symmetry, singular value decomposition (SVD).

A novel approach for designing linear-phase variable two-dimensional (2-D) digital filters is described, which is based on the matrix-array decomposition (MAD) of real-valued multidimensional arrays. By using the MAD, the desired variable 2-D magnitude response can be decomposed into the real-valued frequency response specifications of the normal zero-phase constant 2-D filters and the approximation specifications of multidimensional polynomials. Consequently, the problem of approximating the desired variable 2-D magnitude response can be decomposed into sub-problems that involve the design of zero-phase constant 2-D filters and the approximation of multidimensional polynomials. Once the zero-phase constant 2-D filters and the multidimensional polynomials are obtained, interconnecting them yields a zero-phase variable 2-D digital filter. Finally, a linear-phase variable 2-D digital filter can be easily obtained by simply modifying the zero-phase constant 2-D filters (noncausal) to linear-phase ones (causal) through shifting the filter coefficients. Since the sub-problems are much easier to solve than the direct approximation of the given variable 2-D magnitude specification, this MAD-based design approach is extremely efficient and straightforward. In designing zero-phase constant 2-D filters and approximating multidimensional polynomials, we also propose a new objective criterion for selecting appropriate filter orders and polynomial degrees. Furthermore, we also show that the resulting linear-phase variable 2-D filters have highly parallel structures and modularity, which are suitable for high-speed multidimensional signal processing. Two numerical examples are given to demonstrate the effectiveness of the MAD-based design approach. Index Terms--Linear-phase variable 2-D digital filter, matrix-array decomposition (MAD), variable digital filter, zero-phase constant 2-D digital filter.

In this paper a digital filter is proposed for the generation of smooth set points for motion control systems. The proposed nonlinear filter produces profiles with bounded velocity and acceleration starting from rough reference signals (steps and ramps). An actual implementation of the filter for a tile printing machine is presented and experimental results are reported. Index Terms--Discrete-time filters, motion planning, nonlinear filters, smoothing methods, time-optimal control, tracking filters.

In this brief, results of the sinusoidal response case are presented. It is found that the visual appearance of the trajectory of the sinusoidal response case is much richer than that of the autonomous and step-response cases. Based on the state-space technique, the state vectors to be periodic are investigated. The set of initial conditions and the necessary conditions on the filter parameters are also derived. When overflow occurs, the system is nonlinear. If the corresponding symbolic sequences are periodic, some trajectory patterns are simulated. Since the state-space technique is not sufficient to efficiently derive the sets of initial conditions and the necessary conditions on the filter parameters, a frequency-domain technique is employed to figure out the set of initial conditions. When the symbolic sequences are aperiodic, an elliptical fractal pattern or random-like chaotic pattern is found. Index Terms--Chaotic behavior, second-order digital filter with two's complement arithmetic, sinusoidal response.

In this paper, we examine a new design method for two-dimensional (2-D) recursive digital filters using genetic algorithms (GAs). The design of the 2-D filter is reduced to a constrained minimization problem the solution of which is achieved by the convergence of an appropriate GA. Theoretical results are illustrated by a numerical example. Also, comparison with the results of some previous design methods is attempted. Index Terms--Constrained optimization, genetic algorithm (GA), multidimensional systems, two-dimensional (2-D) recursive filters, 2-D systems.

Variable fractional-delay digital filters are useful in various signal processing applications. To perform both fractional-delay filtering and signal frequency selecting, variable fractional-delay filters must also have variable magnitude characteristics. This paper proposes a method for designing variable finite-impulse response (FIR) filters with both variable magnitude and variable noninteger phase-delay. First, the coefficients of a variable FIR filter are expressed as different 2.variable polynomials of a pair of spectral parameters; one is for varying magnitude response, and the other is for varying noninteger phase-delay. Then the optimal coefficients of the 2-variable polynomials are found by minimizing the total weighted squared error of the variable frequency response. Since the coefficients of the obtained variable FIR filter are the polynomials of the two spectral parameters, we can yield variable magnitude and variable noninteger phase-delay simultaneously or independently by substituting different spectral parameter values to the 2-variable polynomial coefficients. Finally, we show that the resulting variable FIR filter can be implemented in a parallel form, which is suitable for high-speed signal processing. Index Terms--Variable digital filter, variable magnitude, variable noninteger phase-delay.

Since Lim's 1986 paper on the frequency-response-masking (FRM) technique for the design of finite-impulse response digital filters with very small transition widths, the analysis and design of FRM filters has been a subject of study. In this paper, a new optimization technique for the design of various FRM filters is proposed. Central to the new design method is a sequence of linear updates for the design variables, with each update carried out by semidefinite programming. Algorithmic details for the design of basic and multistage FRM filters are presented to show that the proposed method offers a unified design framework for a variety of FRM filters. Design simulations are included to illustrate the proposed algorithms and to evaluate the design performance in comparison with that of several existing methods. Index Terms--Frequency-response-masking filters, optimal design, semidefinite programming.

A novel simultaneous coefficient calculation method for [sinc.sup.N] filter and its application to the filter design are described. This method can be applied to any (N) stages of [sinc.sup.N] filters with no degradation of coefficient accuracy. Every coefficient can be calculated by Nth-order multiple-loop accumulation of N-scaled delayed impulses. The coefficient can be obtained every clock or operation cycle because these loops are not nested but merely chained together. [Sinc.sup.N] decimation filters based on this method are suitable for high-speed operation as well-known cascaded integrator-comb (CIC) filters. If rounding or truncation is used at data-accumulation stages, they can operate faster than those in some cases. For example, the critical-path-length ratio of 32-tap single-bit-input (for delta-sigma analog-to-digital converters) [sinc.sup.4] decimation filters by this and the CIC approach is 0.714 if their outputs are rounded to 8-bit words. Unfortunately, the gate count exponentially increases in proportion to the order N. However, in some special cases (single-bit-input [sinc.sup.2] and [sinc.sup.3] decimation filters), they are comparable to the equivalent CIC filters in size. Index Terms--Cascaded integrator-comb (CIC) filter, decimation, digital filter, interpolation, moving average, sinc, stored coefficient.