Institute for Systems Research Technical Reports

The collection of responses to all elementary ripples is the spectro-temporal transfer function. Previous experiments using ripples with downward drifting spectra suggested that the transfer function is separable, i.e., it is reducible into a product of purely temporal and purely spectral functions.

Here we compare the responses to upward and downward drifting ripples, assuming separability within each direction, to determine if the total bi-directional transfer function is fully separable. In general, the combined transfer function for two directions is not symmetric, and hence units in AI are not, in general, fully separable. Consequently, many AI units have complex response properties such as sensitivity to direction of motion, though most inseparable units are not strongly directionally selective.

We show that for most neurons the lack of full separability stems from differences between the upward and downward spectral cross-sections, not from the temporal cross-sections; this places strong constraints on the neural inputs of these AI units.

We present a computational auditory model that exhibits spectro-temporal MTFs consistent with the salient trends in the data.The model is used to demonstrate the potential relevance of these MTFsto the assessment of speech intelligibility in noise and reverberantconditions.

In this paper, the relationship betweenthe spectro-temporal structure of any given stimulus and the quality ofthe STRF estimate is explored and exploited. Invoking the Fouriertheorem, arbitrary dynamic spectra are described as sums of basicsinusoidal components, i.e., "moving ripples." Accurate estimation isfound to be especially reliant on the prominence of components whosespectral and temporal characteristics are of relevance to the auditorylocus under study, and is sensitive to the phase relationships betweencomponents with identical temporal signatures.

These and otherobservations have guided the development and use of stimuli withdeterministic dynamic spectra composed of the superposition of many"temporally orthogonal" moving ripples having a restricted, relevant rangeof spectral scales and temporal rates.

The method, termedsum-of-ripples, is similar in spirit to the "white-noise approach," butenjoys the same practical advantages--which equate to faster and moreaccurate estimation--attributable to the time-domain sum-of-sinusoidsmethod previously employed in vision research. Application of the methodis exemplified with both modeled data and experimental data from ferretprimary auditory cortex (AI).

Our approach to this problem is based on plant diagonalization.To do this, we search for basis transformations for the vector of outputs coming from the sensors and the vector of inputs applied to the actuators so that, in the new bases, the MIMOsystem becomes a collection of decoupled SISO systems.This formulation provides a number of advantages for the synthesis and implementation of a feedback control law,particularly for systems where the number of inputs and outputs is large.

Of course, in order for this idea to be feasible,the required basis transformations must have properties which allow them to be implemented on a distributed control network. Namely, they must be computed in a distributed manner which respects the spatial distribution of the data(to reduce communication overhead) and takes advantage of the massive parallel processing capability of the network (to reduce computation time).

In this thesis, we present some tools which can be used to find suitable transforms which achieve "approximate"plant diagonalization. We begin by showing how to search the large collection of orthogonal transforms which are contained in the wavelet packet to find the one which most nearly, or approximately, diagonalizes a given real valued matrix.Wavelet packet transforms admit a natural distributed implementation,making them suitable for use on a control network.We then introduce a class of linear operators called recursive orthogonal transforms (ROTs) which we have developed specifically for the purpose of signal processing on distributed control networks.

We show how to use ROTs to approximately diagonalize fixed real and complex matricesas well as transfer function matrices which exhibit a spatial invariance property. Numerical examples of allproposed diagonalization methods are presented and discussed.

We offer a method for computing a workingapproximation to the controllability energy function, one of the mainobjects involved in the method. Moreover, we show that for a class ofsecond-order mechanical systems with dissipation, under certain conditionsrelated to the dissipation, an exact formula for the controllabilityfunction can be derived. We then present an algorithm for a numericalimplementation of the Morse-Palais lemma, which produces a local coordinatetransformation under which a real-valued function with a non-degeneratecritical point is quadratic on a neighborhood of the critical point.

Application of the algorithm to the controllabilty function plays a key rolein computing the balanced representation. We then apply our methods andalgorithms to derive balanced realizations for nonlinear state-space modelsof two example mechanical systems: a simple pendulum and a double pendulum.

The second part (Chapter 5) deals with modeling of rapid thermal chemicalvapor deposition (RTCVD) for growth of silicon thin films, viafirst-principles and empirical analysis. We develop detailedprocess-equipment models and study the factors that influence depositionuniformity, such as temperature, pressure, and precursor gas flow rates,through analysis of experimental and simulation results. We demonstratethat temperature uniformity does not guarantee deposition thicknessuniformity in a particular commercial RTCVD reactor of interest.

In thethird part (Chapter 6) we continue the modeling effort, specializing to acontrol system for RTCVD heat transfer. We then develop and apply ad-hocversions of prominent model reduction approaches to derive reduced modelsand perform a comparative study.

In this work we report on experimentalresults obtained with a deformable tactile sensor whose properties arewell-suited to manipulation. The results presented here show that thesensor described provides a rich set of tactile data.