This PDF file contains the editorial “Editorial: Publication of Proceedings Papers--Revisited” for OE Vol. 31 Issue 06

This PDF file contains the editorial “Guest Editorial: Adaptive Signal Processing” for OE Vol. 31 Issue 06

The concepts of backward consistency and minimality are shown to be the essential tools in studying error propagation in fast least-squares adaptive filters. A conceptual framework identifying the principal error propagation mechanisms is developed, allowing the numerical stability of new or existing algorithms to be ascertained withoutthe technical labor previously thought necessary. The key findings show that arithmetic instability is not a fundamental feature of fast least-squares algorithms. Rather, unstable propagation can only derive from the violation of backward consistency constraints. The absence of minimality (in the system theory sense) is identified as the principal culprit in this regard, although the issue of stability for predictable sequences also plays an intriguing role. The concepts are illustrated for some popularly used algorithms, and order-recursive algorithms are confirmed to have intrinsic advantages over their transversal counterparts.

A new approach for the analysis of the propagation of roundoff errors in recursive algorithms is presented. This approach is based on the concept of backward consistency. In general, this concept leads to a decomposition of the state space of the algorithm, and in fact, to a manifold. This manifold is the set of state values that are backward consistent. Perturbations within the manifold can be interpreted as resulting from perturbations on the input data. Hence, the error propagation on the manifold corresponds exactly (without averaging or even linearization) to the propagation of the effect of a perturbation of the input data at some point in time on the state of the algorithm at future times. We apply these ideas to the Kalman filter and its various derivatives. In particular, we consider the conventional Kalman filter, some minor variations of it, and its square-root forms. Next we consider the Chandrasekhar equations, which apply to time-invariant state-space models. Recursive least-squares (RLS) parameter estimation is a special case of Kalman filtering, and hence the previous results also apply to the RLS algorithms. We also consider in detail two groups of fast RLS algorithms: the fast transversal filter algorithms and the fast lattice/fast QR RLS algorithms.

We analyze the finite precision properties ofa QR-decomposition-based adaptive lattice filter used as a linear one-step predictor implemented using fixed-point arithmetic. We present equations for the steadystate mean-squared values of the accumulated numerical errors in the computations of the algorithm. Our analysis indicates that the numerical inaccuracy associated with some of the variables in the algorithm increases with increasing values of the exponential weighting factor employed by the adaptive filter. However, there are some other variables whose numerical accuracy increases with increasing values of the exponential weighting factor, indicating that different variables in the algorithm may need to be implemented with different precisions to obtain the desired numerical accuracy. The analysis also shows that the numerical errors, in general, increase from stage to stage. The errors tend to be larger for highly correlated signals than for signals with less correlation between neighboring samples. We also present experimental verification of the analytical results. The predicted and experimental results show close agreement for practical values of the weighting factor and precision used in the implementation of the adaptive filter.

Stop-and-go adaptation rules that are utilized to improve the blind convergence characteristics of the conventional and sign decision-directed algorithms are proposed and examined. They are based on the Sato- and Godard-type errors, which are utilized in many blind deconvolution applications. The convergence rates achieved by the algorithms with quadrature amplitude modulated signal constellations and nonminimum phase communication channels are compared. Based on a new criterion, the optimal values of the Sato and Godard error parameters are redefined. The optimality of the new parameter values is confirmed by means of computer simulations.

Blind adaptive channel equalizers are important devices to remove channel distortion in high data-rate, bandlimited digital communication systems when the transmission of a training sequence is impractical or very costly. Traditional blind equalization algorithms adapt the equalizer parameters to minimize some specially designed non-MSE cost functions. These algorithms can experience local convergence problems and can thereby result in insufficient or no removal of channel distortion. We present a new quadrature amplitude modulated blind equalization scheme that is globally convergent in the equalizer parameter space to a compact set containing the desired ideal equalizer parameter setting. Our new algorithm is based on a convex cost function and a linear constraint on the equalizer parameters. For a generic class of channels, this new algorithm results in the equalizer parameter convergence to a unique global minimum achieving intersymbol interference suppression and carrier phase error removal. Different implementation approaches are assessed and simulation results are shown to confirm the theoretical global convergence of the new algorithm.

Blind equalization methods usually combat the linear distortion caused by a nonideal channel via a transversal filter, without resorting to the a priori known training sequence. We introduce a new criterion with memory nonlinearity (CRIMNO) for the blind equalization problem. The basic idea of this criterion is to augment the Godard [or constant modulus algorithm (CMA)] cost function with additional terms that penalize the autocorrelations of the equalizer outputs. Several variations of the CRIMNO algorithm are derived, with the variations dependent on (1) whether the empirical averages or the single point estimates are used to approximate the expectations, (2) whether the recent or the delayed equalizer coefficients are used, and (3) whether the weights applied to the autocorrelation terms are fixed or are allowed to adapt. Simulation experiments show that the CRIMNO algorithm, and especially its adaptive weight version, exhibits faster convergence speed than the Godard (or CMA) algorithm. Extensions of the CRIMNO criterion to accommodate the case of correlated inputs to the channel are also presented.

A new blind equalization algorithm is presented that incorporates a Bayesian channel estimator and a decision-feedback (DF) adaptive filter. The Bayesian algorithm operates as a preprocessor on the received signal to provide an initial estimate of the channel coefficients. It is an approximate maximum a posteriori (MAP) sequence estimator that generates reliable estimates of the transmitted symbols. These decisions are then filtered by an adaptive decision-feedback algorithm to further reduce the intersymbol interference. The new algorithm is more robustto catastrophic error propagation thanthe standard decision-feedback equalizer (DFE), with only a modest increase in the computational complexity.

A new approach to blind equalization is investigated in which the receiver performs joint data and channel estimation in an iterative manner. Instead of estimating the channel inverse, the receiver computes the maximum-likelihood estimate of the channel itself. The iterative algorithm that is developed involves maximum-likelihood sequence estimation (Viterbi decoding) for the data estimation part, and least-squares estimation for the channel estimation part. A suboptimal algorithm is also proposed that uses a reduced-state trellis instead of the Viterbi algorithm. Simulation results show that the performance obtained by these algorithms is comparable to that of a receiver operating with complete knowledge of the channel.

Compactly supported wavelet bases are sets of compactly supported functions that are orthonormal bases for a wide variety of function spaces, including signals that have finite energy or finite power. The theory of compactly supported wavelets is placed in its historical context. Wavelet matrices and wavelet functions of one and two variables are defined. The continuous, discrete, and finite wavelet transforms are contrasted with the corresponding Fourier transforms. A multirate digital filter interpretation is provided, and adaptive trees of wavelet filters are described.

We have observed that if one restricts the von Neumann lattice to N points on the time axis and M points in the frequency axis there are, by definition, only MN independent Gabor coefficients. If the data is sampled such thatthere are exactly MN samples, then the forward and inverse Gabor transforms should be representable as linear transformations in C_MN, the MN-dimensional vector space over the complex numbers, and the relationships that hold become matrix equations. These matrix equations are formulated, and some conclusions are drawn about the relative merits of using some methods as opposed to others, i.e., speed versus accuracy as well as whether or not the coefficients that are obtained via some methods are true Gabor coefficients.

The "chirplet" transform unifies manyof the disparate signal representation methods. In particular, the wide ra nge of time-frequency (TF) methods such as the Fourier transform, spectrogram, Wigner distribution, ambiguity function, wideband ambiguity function, and wavelet transform may each be shown to be a special case of the chirplet transform. The above-mentioned TF methods as well as many new ones may be derived by selecting appropriate 2-D manifolds from within the 8-D "chirplet space" (with appropriate smoothing kernel). Furthermore, the chirplet transform is a framework for deriving new signal representations. The chirplet transform is a mapping from a 1-D domain to an 8-D range (in contrast to the wavelet, for example, which is a 1-D to 2-D mapping). Display of the 8-D space is at best difficult. (Although it may be displayed by moving a mesh around in a 3-D virtual world, the whole space cannot be statically displayed in its entirety.) Computation of the 8-D range is also difficult. The adaptive chirplet transform attempts to alleviate some of these problems by selecting an optimal set of bases without the need to manually intervene. The adaptive chirplet, based on expectation maximization, may also form the basis for a classifier (such as a radial basis function neural network) in TF space.

The procedure followed in optimizing a five-element diffraction- limited laser scan lens to eliminate one of the elements is described. The starting procedure uses thicknesses found in the five-element design except for the two central positive elements, which are combined to make a single thick third element. The resulting four-element lens employs high-index glass for each element and achieves diffraction-limited performance.

A highly efficient phase-only hologram has been produced using an ion-exchange method. An optimum condition for the phase profile of the hologram is described. The ion density and the phase profile generated by the ion exchange were calculated by computer simulations. The diffraction patterns of different gratings are calculated based on these data, and an optimum phase distribution is estimated. The optimum condition has been verified experimentally.

Computer vision is a task of information processing that can be modeled as a sequence of subtasks. A complete vision process can be constructed by synthesizing individual operators performing the subtasks. Previous work in computer vision has emphasized the development of individual operators for a specific subtask. However, the lack of knowledge about other levels of processing, while developing the operators for a specific level, makes the development of a robust operator and thus a robust system unlikely. To obtain vision problem-solving methods that are robust in the face of variations in image lighting, arrangements of objects, viewing parameters, etc., we can simply incorporate all possible sequences of image-processing operators, each of which deals with a specific situation of input images; then an adaptive control mechanism such as a state-space search procedure can be built into the methods. Such a procedure dynamically determines an optimal sequence of image-processing operators to classify an image or to put its parts into correspondence with a model or set of models. One critical problem in solving vision problems with a state-space search model is how to decide the costs of paths. This paper details the state-space search model of computer vision as well as the design of cost functions in terms of information distortions. A vision system, VISTAS, has been constructed under the state-space search model and its parallel version has been simulated.

This paper presents efficient filtering algorithms for the interpolation of sequences using IIR filters. Of the suggested filters, the most efficient in terms of computational complexity consists of a very simple allpass IIR filter in parallel with a pure delay. The nonlinear phase distortions of IIR filters, particularly severe in image processing, are avoided by a zero-phase implementation obtained by a combination of causal and anticausal filters. The proposed approach is more efficient for image zooming applications than other methods and yields visually satisfactory results for most gray-scale images.

The introduction of optics into the field of artificial intelligence is an important new trend. Optics has some inherent advantages such as parallel propagation, etc., which can be fully exploited especially in computer vision and pattern recognition. Similarly, in intelligent information processing where information is kept in well-formed expressions (sentences), optics can offer sufficient advantages. A method is proposed in which a well-formed expression is converted into an optical binary data form, which could possibly be better and easier for the computer to handle and access intelligent expressions. To perform this conversion, the tree-architecture-based system is shown to be very useful.

A review of various types of active and passive mode-locked lasers is presented. Theoretical and experimental aspects of mode locking are covered. Stabilization schemes used in mode-locked laser systems are described. Techniques used in the measurement of the time duration of the ultrashort pulses and the uses of high-power, low-power, and picosecond pulses are given.

Definitions of centerline and centerline overlay (O/L) are built on the implicit assumptions of certain symmetries. Verification of these symmetries, and the use of redundancies built into the design of O/L measurement marks, can estimate the relative accuracy of O/L measurements, even in the absence of certified reference materials (standards). Verification carried out as of paired comparison is shown to be very effective; in addition, it constitutes the basis for data culling. Several sources of O/L measurement inaccuracy, associated with O/L measurement tools and with O/L measurement marks, are pointed out and some are illustrated using modeling. A simple measure of tool-related inaccuracy, tool-induced shift (TIS), is proposed and utilized as a performance estimate of O/L measurement tools relative to accuracy. Inaccuracies of O/L measurements, caused by O/L measurement tools and marks, on the order of 100 nm, are observed and their causes identified. Examples are given of significant improvements in accuracy. A roadmap toward accurate O/L measurement is outlined. This approach is also applicable to alignment systems.

Microlens arrays are a component of atmospheric wavefront sensors used recently with success by ground-based astronomers to obtain diffraction-limited images of stars in spite of wavefront disturbances introduced by the earth's atmosphere. Typical requirements for individual lenses are a size measured in tenths of millimeters, a sag measured in micrometers, and no room left between lenses, i.e., square or hexagonal lenses rather than circular lenses. Actual monolithic square microlens arrays up to 20 x 20 mm in size for 0.18- to 1.5-mm individual contiguous lenses of 0.0035-mm maximum sag are engraved in photoresist coatings by a two-axes rastering process. These arrays have been used for diurnal and nocturnal atmospheric wavefront measurements.

A connectorized integrated N x N passive star coupler suitable for use in single-mode multichannel optical networks is reported. The excess loss for most of the channels of the coupler is within 1.5 dB, with a worst value of 3 dB, of the unconnectorized coupling values, which range from 14.5 to 17.5 dB. The optical fibers are attached to the 19 x 19 coupler by butt-coupling a linear array of single-mode fibers using silicon v-grooves. Alignment is rapidly achieved with a compact six-degrees-of-freedom piezo-controlled micromanipulator. Best values of less than 0.1 dB per fiber attachment, dependent on connector quality, were obtained. The coupler demonstrated negligible reflection effects when used as the central element in a 1-Gb/s frequency-division-multiplex network experiment.

The exact field solution of a step-index profile fiber was used to determine the excitation efficiency of a distribution of sources in the core of an optical fiber. We have compared previous results of a thin-film cladding source distribution to its core source counterpart. The behavior of power efficiency P_eff with the fiber parameters was examined and found to be similar to the behavior exhibited by cladding sources. It was also found that a core source fiber is two orders of magnitude more efficient than a fiber with a bulk distribution of cladding sources. This result agrees, qualitatively, with previous ones obtained experimentally.

Axial strain can be determined by monitoring the modal pattern variation of an optical fiber. The results of a numerical model developed to calculate the modal pattern variation at the end of a weakly guiding optical fiber under axial strain is presented. Whenever an optical fiber is under stress, the optical path length, the index of refraction, and the propagation constants of each fiber mode change. In consequence, the modal phase term β_inz of the fields and the fiber output pattern are also modified. For multimode fibers, very complicated patterns result. The predicted patterns are presented and an expression for the phase variation with strain is derived