Analysis of spectroscopic measurements of leaf water content at terahertz frequencies using linear transforms

We provide a unified framework for a range of linear transforms that can be used for the analysis of terahertz spectroscopic data, with particular emphasis on their application to the measurement of leaf water content. The use of linear transforms for filtering, regression, and classification is discussed. For illustration, a classification problem involving leaves at three stages of drought and a prediction problem involving simulated spectra are presented. Issues resulting from scaling the data set are discussed. Using Lagrange multipliers, we arrive at the transform that yields the maximum separation between the spectra and show that this optimal transform is equivalent to computing the Euclidean distance between the samples. The optimal linear transform is compared with the average for all the spectra as well as with the Karhunen–Loève transform to discriminate a wet leaf from a dry leaf. We show that taking several principal components into account is equivalent to defining new axes in which data are to be analyzed. The procedure shows that the coefficients of the Karhunen–Loève transform are well suited to the process of classification of spectra. This is in line with expectations, as these coefficients are built from the statistical properties of the data set analyzed.

On-line handwritten segmentation in linear drawings

This paper addresses the problem of tracking line segments corresponding to on-line handwritten obtained through a digitizer tablet. The approach is based on Kalman filtering to model linear portions of on-line handwritten, particularly, handwritten numerals, and to detect abrupt changes in handwritten direction underlying a model change. This approach uses a Kalman filter framework constrained by a normalized line equation, where quadratic terms are linearized through a first-order Taylor expansion. The modeling is then carried out under the assumption that the state is deterministic and time-invariant, while the detection relies on double thresholding mechanism which tests for a violation of this assumption. The first threshold is based on an approach of layout kinetics. The second one takes into account the jump in angle between the past observed direction of layout and its current direction. The method proposed enables real-time processing. To illustrate the methodology proposed, some results obtained from handwritten numerals are presented.

Composite control of non-linear singularly perturbed systems: meeting a design objective

Using the integral manifold approach, a composite control—the sum of a fast control and a slow control—is derived for a particular class of non-linear singularly perturbed systems. The fast control is designed completely at the outset, thus ensuring the stability of the fast transients of the system and, furthermore, the existence of the integral manifold. A new method is then presented which simplifies the derivation of a slow control such that the singularly perturbed system meets a preselected design objective to within some specified order of accuracy. Though this approach is, by its very nature, ad hoc, the underlying procedure is easily extended to more general classes of singularly perturbed systems by way of three examples.

Structure adaptation of linear MMSE adaptive filters

The tap-length, or the number of the taps, is an important structural parameter of the linear MMSE adaptive filter. Although the optimum tap-length that balances performance and complexity varies with scenarios, most current adaptive filters fix the tap-length at some compromise value, making them inefficient to implement especially in time-varying scenarios. A novel gradient search based variable tap-length algorithm is proposed, using the concept of the pseudo-fractional tap-length, and it is shown that the new algorithm can converge to the optimum tap-length in the mean. Results of computer simulations are also provided to verify the analysis.

An adaptive linear equalizer with optimum filter length and decision delay

The power of an adaptive equalizer is maximized when the structural parameters including the tap-length and decision delay can be optimally chosen. Although the method for adjusting either the tap-length or decision delay has been proposed, adjusting both simultaneously becomes much more involved as they interact with each other. In this paper, this problem is solved by putting a linear prewhitener before the equalizer, with which the equivalent channel becomes maximum-phase. This implies that the optimum decision delay can be simply ¯xed at the tap-length minus one, while the tap-length can then be chosen using a similar approach as that proposed in our previous work.

Optimal control of a class of discrete–continuous non-linear systems — decomposition and hierarchical structure

A technique is derived for solving a non-linear optimal control problem by iterating on a sequence of simplified problems in linear quadratic form. The technique is designed to achieve the correct solution of the original non-linear optimal control problem in spite of these simplifications. A mixed approach with a discrete performance index and continuous state variable system description is used as the basis of the design, and it is shown how the global problem can be decomposed into local sub-system problems and a co-ordinator within a hierarchical framework. An analysis of the optimality and convergence properties of the algorithm is presented and the effectiveness of the technique is demonstrated using a simulation example with a non-separable performance index.

Linear-wavelet models for non-linear identification applied to a pressure plant

A nonlinear regression structure comprising a wavelet network and a linear term is proposed for system identification. The theoretical foundation of the approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such models is described and the approach is tested with experimental data.

Linear-wavelet models applied to the identification of a two-link manipulator

This paper shows that a wavelet network and a linear term can be advantageously combined for the purpose of non linear system identification. The theoretical foundation of this approach is laid by proving that radial wavelets are orthogonal to linear functions. A constructive procedure for building such nonlinear regression structures, termed linear-wavelet models, is described. For illustration, sim ulation data are used to identify a model for a two-link robotic manipulator. The results show that the introduction of wavelets does improve the prediction ability of a linear model.

Linear-wavelet models for system identification

A model structure comprising a wavelet network and a linear term is proposed for nonlinear system identification. It is shown that under certain conditions wavelets are orthogonal to linear functions and, as a result, the two parts of the model can be identified separately. The linear-wavelet model is compared to a standard wavelet network using data from a simulated fermentation process. The results show that the linear-wavelet model yields a smaller modelling error when compared to a wavelet network using the same number of regressors.

Infrared linear dichroism spectroscopy on amyloid fibrils aligned by molecular combing

We report the use of molecular combing as an alignment method to obtain macroscopically oriented amyloid fibrils on planar surfaces. The aligned fibrils are studied by polarized infrared spectroscopy. This gives structural information that cannot be definitively obtained from standard infrared experiments on isotropic samples, for example, confirmation of the characteristic cross-beta amyloid core structure, the side-chain orientation from specific amino acids, and the arrangement of the strands within the fibrils, as we demonstrate here. We employed amyloid fibrils from hen egg white lysozyme (HEWL) and from a model octapeptide. Our results demonstrate molecular combing as a straightforward method to align amyloid fibrils, producing highly anisotropic infrared linear dichroism (IRLD) spectra.