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Closed Loop Identification Of A First Order Plus Dead-Time Process Model Under Pi Control, Tony Kealy, Aidan O'Dwyer Jan 2002

Closed Loop Identification Of A First Order Plus Dead-Time Process Model Under Pi Control, Tony Kealy, Aidan O'Dwyer

Conference papers

This paper discusses the estimation of the parameters of a first order plus dead-time process model using the closed-loop step response data of the process under proportional plus integral (PI) control. The proportional gain and the integral time, in the PI controller, are chosen such that the closed-loop step response exhibits an under-damped response. From this response data, five characteristic points are used to determine a second order plus dead-time model and subsequently, the frequency response of the closed-loop system. Knowing the dynamics of the closed-loop system and the dynamics of the controller, the open-loop dynamics of the process can …

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Comparison Of Mlp And Rbf Neural Networks Using Deviation Signals For On-Line Identification Of A Synchronous Generator, Jung-Wook Park, Ganesh K. Venayagamoorthy, Ronald G. Harley Jan 2002

Comparison Of Mlp And Rbf Neural Networks Using Deviation Signals For On-Line Identification Of A Synchronous Generator, Jung-Wook Park, Ganesh K. Venayagamoorthy, Ronald G. Harley

Electrical and Computer Engineering Faculty Research & Creative Works

This paper compares the performances of a multilayer perceptron network (MLPN) and a radial basis function network (RBFN) for the online identification of the nonlinear dynamics of a synchronous generator. Deviations of signals from their steady state values are used. The computational complexity required to process the data for online training, generalization and online global minimum testing are investigated by time-domain simulations. The simulation results show that, compared to the MLPN, the RBFN is simpler to implement, needs less computational memory, converges faster and global minimum convergence is achieved even when operating conditions change.

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Tissue Classification Through Analysis Of Gene Expression Data Using A New Family Of Art Architectures, Rui Xu, Georgios C. Anagnostopoulos, Donald C. Wunsch Jan 2002

Tissue Classification Through Analysis Of Gene Expression Data Using A New Family Of Art Architectures, Rui Xu, Georgios C. Anagnostopoulos, Donald C. Wunsch

Electrical and Computer Engineering Faculty Research & Creative Works

Correct classification is crucial to cancer diagnosis and treatment. We demonstrate that a new family of neural network architectures-Ellipsoid ART and ARTMAP (EA/EAM)-can cluster and classify tissues successfully through analysis of gene expression data generated by DNA microarray experiments

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A Diode-Clamped Multi-Level Inverter For The Statcom/Bess, Cheng Ying, Mariesa Crow Jan 2002

A Diode-Clamped Multi-Level Inverter For The Statcom/Bess, Cheng Ying, Mariesa Crow

Electrical and Computer Engineering Faculty Research & Creative Works

Flexible AC transmission systems (FACTS) are potentially becoming more flexible and more economical local controllers in the power system. The integration of traditional FACTS devices with energy storage system (ESS) will increase FACTS device functionality. The voltage-sourced inverter is an important part of many FACTS devices, such as the StatCom and SSSC. Considerable research has been done on 2-level inverter usage in FACTS. Multilevel inverters, however, can improve the voltage quality and reduce the voltage stress on the power electronic devices. This paper uses a diode-clamped multilevel inverter in the StatCom/BESS. The multilevel inverter switching strategy and output voltage model …

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Sub-Band Independent Subspace Analysis For Drum Transcription, Derry Fitzgerald, Robert Lawlor, Eugene Coyle Jan 2002

Sub-Band Independent Subspace Analysis For Drum Transcription, Derry Fitzgerald, Robert Lawlor, Eugene Coyle

Conference papers

While Independent Subspace Analysis provides a means of separating sound sources from a single channel signal, making it an effective tool for drum transcription, it does have a number of problems. Not least of these is that the amount of information required to allow separation of sound sources varies from signal to signal. To overcome this indeterminacy and improve the robustness of transcription an extension of Independent Subspace Analysis to include sub-band processing is proposed. The use of this approach is demonstrated by its application in a simple drum transcription algorithm.

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Finite-Element Modeling Of Coaxial Cable Feeds And Vias In Power-Bus Structures, Hao Wang, Yun Ji, Todd H. Hubing Jan 2002

Finite-Element Modeling Of Coaxial Cable Feeds And Vias In Power-Bus Structures, Hao Wang, Yun Ji, Todd H. Hubing

Electrical and Computer Engineering Faculty Research & Creative Works

This paper presents three different models that can be used to represent coaxial cable feeds or vias in printed circuit board power-bus structures. The probe model represents a coaxial feed or via as a current filament with unknown radius. The coaxial-cable model enforces an analytical field distribution at the cable opening or via clearance hole. The strip model employs the equivalent radius concept to represent cylindrical feeds and vias as rectangular strips. Although the strip model is functionally equivalent to two closely positioned probe models, it accurately represents the conductor radius and is more accurate in situations where the via …

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Measurement And Monitoring Of Microwave Reflection And Transmission Properties Of Cement-Based Specimens, Sergey Kharkovsky, M. F. Akay, U. C. Hasar, C. D. Atis Jan 2002

Measurement And Monitoring Of Microwave Reflection And Transmission Properties Of Cement-Based Specimens, Sergey Kharkovsky, M. F. Akay, U. C. Hasar, C. D. Atis

Electrical and Computer Engineering Faculty Research & Creative Works

The results of measurement and monitoring of reflection and transmission properties of cement-based specimens (blocks of mortar, concrete) obtained by using a simple and an inexpensive measurement system at microwave frequencies (X-band) are presented. Dependencies of the reflection and transmission coefficients on water-to-cement (w/c) ratio, preparing and curing conditions of the specimens are demonstrated. It is shown that the amplitudes of reflection and transmission coefficients, together with thickness of the specimens, determine the complex dielectric permittivity of the hardened cement-based specimens. The expected applications of the results for the determination of physical properties of cement-based materials are discussed. The causes …

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On The Modeling Of A Gapped Power-Bus Structure Using A Hybrid Fem/Mom Approach, Yun Ji, Todd H. Hubing Jan 2002

On The Modeling Of A Gapped Power-Bus Structure Using A Hybrid Fem/Mom Approach, Yun Ji, Todd H. Hubing

Electrical and Computer Engineering Faculty Research & Creative Works

A hybrid finite-element-method/method-of-moments (FEM/MoM) approach is applied to the analysis of a gapped power-bus structure on a printed circuit board. FEM is used to model the details of the structure. MoM is used to provide a radiation boundary condition to terminate the FEM mesh. Numerical results exhibit significant errors when the FEM/MoM boundary is chosen to coincide with the physical boundary of the board. These errors are due to the inability of hybrid elements on the boundary to enforce the correct boundary condition at a gap edge in a strong sense. A much better alternative is to extend the MoM …

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Analysis Of A Four-Level Dc/Dc Buck Converter, Keith Corzine, J. Yuen, J. R. Baker Jan 2002

Analysis Of A Four-Level Dc/Dc Buck Converter, Keith Corzine, J. Yuen, J. R. Baker

Electrical and Computer Engineering Faculty Research & Creative Works

In this paper, a four-level DC/DC buck power converter is introduced. The primary application for this converter is to regulate the center capacitor voltage in a four-level inverter system. The steady-state and average-value models for the proposed converter are developed and compared in simulation. The converter was constructed in the laboratory and verified on a four-level motor drive system. It was shown that the four-level DC/DC converter provides capacitor voltage balancing and allows higher output voltage utilization from the inverter.

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Restoration Of The Lorentzian And Debye Curves Of Dielectrics And Magnetics For Fdtd Modeling, Marina Koledintseva, Konstantin Rozanov, James L. Drewniak, Gabriele Di Fazio Jan 2002

Restoration Of The Lorentzian And Debye Curves Of Dielectrics And Magnetics For Fdtd Modeling, Marina Koledintseva, Konstantin Rozanov, James L. Drewniak, Gabriele Di Fazio

Electrical and Computer Engineering Faculty Research & Creative Works

The algorithms of extracting the Lorentzianand Debye-curve parameters of dielectric and magnetic materials from the results of measurements at several frequency points are presented. These algorithms are based on an analytical solution of systems of non-linear equations with physical constraints that follow from the fundamental principle of causality. The extracted parameters are useful for FDTD modeling of electromagnetic structures containing such dispersive media. Some examples are presented.

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Memory Optimization Techniques For Embedded Systems, Jinpyo Hong Jan 2002

Memory Optimization Techniques For Embedded Systems, Jinpyo Hong

LSU Doctoral Dissertations

Embedded systems have become ubiquitous and as a result optimization of the design and performance of programs that run on these systems have continued to remain as significant challenges to the computer systems research community. This dissertation addresses several key problems in the optimization of programs for embedded systems which include digital signal processors as the core processor. Chapter 2 develops an efficient and effective algorithm to construct a worm partition graph by finding a longest worm at the moment and maintaining the legality of scheduling. Proper assignment of offsets to variables in embedded DSPs plays a key role in …

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Modulation Classification Of Digital Communication Signals, Visalakshi S. Ramakonar Jan 2002

Modulation Classification Of Digital Communication Signals, Visalakshi S. Ramakonar

Theses: Doctorates and Masters

Modulation classification of digital communications signals plays an important role in both military and civilian sectors. It has the potential of replacing several receivers with one universal receiver. An automatic modulation classifier can be defined as a system that automatically identifies the modulation type of the received signal given that the signal exists and its parameters lie in a known range. This thesis addresses the need for a universal modulation classifier capable of classifying a comprehensive list of digital modulation schemes. Two classification approaches are presented: a decision-theoretic (DT) approach and a neural network (NN) approach. First classifiers are introduced …

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Reliability Of Programmable Input/Output Pins In The Presence Of Configuration Upsets, Paul S. Graham, Nathaniel Rollins, Michael J. Wirthlin, Michael P. Caffrey Jan 2002

Reliability Of Programmable Input/Output Pins In The Presence Of Configuration Upsets, Paul S. Graham, Nathaniel Rollins, Michael J. Wirthlin, Michael P. Caffrey

Faculty Publications

Sponsorship: Los Alamos National Laboratories (LA-UR-02-3163). Field programmable gate arrays (FPGAs) are an attractive alternative for space-based remote sensing applications. However, SRAM-based FPGAs are sensitive to radiation induced single-event upsets within the configuration memory. Such configuration upsets may change the logic, routing, and operating modes of a user FPGA design. Upsets within the configuration of an I/O block are especially troublesome as they may impact the operation of other system components. This paper will evaluate the operation of the I/O block within the Xilinx Virtex FPGA in the presence of configuration memory upsets and introduce techniques for detecting and repairing …

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Two-Dimensional Fast Evanescent Wave Algorithm, W. C. Chew, L. (Lijun) J. Jiang, S. Velamparambil Dec 2001

Two-Dimensional Fast Evanescent Wave Algorithm, W. C. Chew, L. (Lijun) J. Jiang, S. Velamparambil

Electrical and Computer Engineering Faculty Research & Creative Works

A new fast evanescent wave algorithm (FEWA) is introduced in the two-dimensional (2-D) case. It expands the Green's function into propagating waves and directional evanescent waves. Applying the evanescent wave correction technique, a procedure similar to the traditional MLFMA can be expedited. No buffer region is necessary anymore, and fewer translators are needed. Numerical examples are given to show the features of this method.

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Applying Time-Frequency Distribution Function To Doa Of Mobile Active Sensor, Shun-Hsyung Chang, Jun-Cheng Liu, Chih-Wei Chiu Dec 2001

Applying Time-Frequency Distribution Function To Doa Of Mobile Active Sensor, Shun-Hsyung Chang, Jun-Cheng Liu, Chih-Wei Chiu

Journal of Marine Science and Technology–Taiwan

Increasing the accuracy of time-frequency detection in engineering is always the goal that scientists are striving to achieve, because it is widely applied in the fields of Radar, Sonar, the exploration of earthquake epicenter etc. The current high-resolution time-frequency methods are mostly based on the structure of time-frequency distribution function of Cohen Family. Time frequency distribution function can trace the instantaneous frequency of nonstationary signal. This paper combines the process principle of multi-aperture Radar and Array signal and applies time-frequency distribution function in DOA of active sensor devices. By decoding of physical characteristics from the changes of frequency, which can …

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Nonlinear Suppression Of Range Ambiguity In Pulse Doppler Radar, Jon M. Anderson Dec 2001

Nonlinear Suppression Of Range Ambiguity In Pulse Doppler Radar, Jon M. Anderson

Theses and Dissertations

Coherent pulse train processing is most commonly used in airborne pulse Doppler radar, achieving adequate transmitter/receiver isolation and excellent resolution properties while inherently inducing ambiguities in Doppler and range. First introduced by Palermo in 1962 using two conjugate LFM pulses, the primary nonlinear suppression objective involves reducing range ambiguity, given the waveform is nominally unambiguous in Doppler, by using interpulse and intrapulse coding (pulse compression) to discriminate received ambiguous pulse responses. By introducing a nonlinear operation on compressed (undesired) pulse responses within individual channels, ambiguous energy levels are reduced in channel outputs. This research expands the NLS concept using discrete …

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Survivable Mobile Operating System, James Whittaker, Mohommad Samarah Dec 2001

Survivable Mobile Operating System, James Whittaker, Mohommad Samarah

Electrical Engineering and Computer Science Faculty Publications

Although there is a large body of work on cryptographic techniques and algorithms that provide basic building blocks to solve specific security problems, relatively little work has been done in investigating security issues in mobile system contexts. Conventional security controls work well for static code, but break down with code mobility. In this paper, we investigate the need for end-to-end security in mobile and wireless operating systems. We study the implications of mobility - specifically, ways in which the operating system may facilitate communication security. We suggest a framework for designing security into mobile devices by building encryption into the …

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Techniques For The Regeneration Of Wideband Speech From Narrowband Speech, Jason A. Fuemmeler, Russell C. Hardie, William R. Gardner Dec 2001

Techniques For The Regeneration Of Wideband Speech From Narrowband Speech, Jason A. Fuemmeler, Russell C. Hardie, William R. Gardner

Electrical and Computer Engineering Faculty Publications

This paper addresses the problem of reconstructing wideband speech signals from observed narrowband speech signals. The goal of this work is to improve the perceived quality of speech signals which have been transmitted through narrowband channels or degraded during acquisition. We describe a system, based on linear predictive coding, for estimating wideband speech from narrowband. This system employs both previously identified and novel techniques. Experimental results are provided in order to illustrate the system’s ability to improve speech quality. Both objective and subjective criteria are used to evaluate the quality of the processed speech signals.

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Projection-Based Image Registration In The Presence Of Fixed-Pattern Noise, Ernest Armstrong, Stephen C. Cain, Majeed M. Hayat Dec 2001

Projection-Based Image Registration In The Presence Of Fixed-Pattern Noise, Ernest Armstrong, Stephen C. Cain, Majeed M. Hayat

Electrical and Computer Engineering Faculty Research and Publications

A computationally efficient method for image registration is investigated that can achieve an improved performance over the traditional two-dimensional (2-D) cross-correlation-based techniques in the presence of both fixed-pattern and temporal noise. The method relies on transforming each image in the sequence of frames into two vector projections formed by accumulating pixel values along the rows and columns of the image. The vector projections corresponding to successive frames are in turn used to estimate the individual horizontal and vertical components of the shift by means of a one-dimensional (1-D) cross-correlation-based estimator. While gradient-based shift estimation techniques are computationally efficient, they often …

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Energy Storage Systems For Advanced Power Applications, Aysen Arsoy, Yilu Liu, Paul F. Ribeiro, Brian K. Johnson, Mariesa Crow Dec 2001

Energy Storage Systems For Advanced Power Applications, Aysen Arsoy, Yilu Liu, Paul F. Ribeiro, Brian K. Johnson, Mariesa Crow

Electrical and Computer Engineering Faculty Research & Creative Works

While energy storage technologies do not represent energy sources, they provide valuable added benefits to improve stability power quality, and reliability of supply. Battery technologies have improved significantly in order to meet the challenges of practical electric vehicles and utility applications. Flywheel technologies are now used in advanced nonpolluting uninterruptible power supplies. Advanced capacitors are being considered as energy storage for power quality applications. Superconducting energy storage systems are still in their prototype stages but receiving attention for utility applications. The latest technology developments, some performance analysis, and cost considerations are addressed. This paper concentrates on the performance benefits of …

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Greenland Snow Accumulation Estimates From Satellite Radar Scatterometer Data, Mark R. Drinkwater, David G. Long, Andrew W. Bingham Dec 2001

Greenland Snow Accumulation Estimates From Satellite Radar Scatterometer Data, Mark R. Drinkwater, David G. Long, Andrew W. Bingham

Faculty Publications

Data collected by the C band ERS-2 wind scatterometer (EScat), the Ku band ADEOS-1 NASA scatterometer (NSCAT), and the Ku band SeaWinds on QuikScat (QSCAT) satellite instruments are used to illustrate spatiotemporal variability in snow accumulation on the Greenland ice sheet. Microwave radar backscatter images of Greenland are derived using the scatterometer image reconstruction (SIR) method at 3-day intervals over the periods 1991–1998 and 1996–1997 for EScat and NSCAT, respectively. The backscatter coefficient σ° normalized to 40° incidence, A, and gradient in backscatter, B, in the range 20°–60° are compared with historical snow accumulation data and recent measurements …

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Phad: Packet Header Anomaly Detection For Identifying Hostile Network Traffic, Philip K. Chan, Matthew V. Mahoney Nov 2001

Phad: Packet Header Anomaly Detection For Identifying Hostile Network Traffic, Philip K. Chan, Matthew V. Mahoney

Electrical Engineering and Computer Science Faculty Publications

We describe an experimental packet header anomaly detector (PHAD) that learns the normal range of values for 33 fields of the Ethernet, IP, TCP, UDP, and ICMP protocols. On the 1999 DARPA off-line intrusion detection evaluation data set (Lippmann et al. 2000), PHAD detects 72 of 201 instances (29 of 59 types) of attacks, including all but 3 types that exploit the protocols examined, at a rate of 10 false alarms per day after training on 7 days of attack-free internal network traffic. In contrast to most other network intrusion detectors and firewalls, only 8 attacks (6 types) are detected …

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Mechanical, Geometrical, And Electrical Characterization Of Silicon Membranes For Open Stencil Masks, E. Sossna, A. Degen, I. W. Rangelow, M. Drzik, P. Hudek, T. E. Tiwald, John A. Woollam Nov 2001

Mechanical, Geometrical, And Electrical Characterization Of Silicon Membranes For Open Stencil Masks, E. Sossna, A. Degen, I. W. Rangelow, M. Drzik, P. Hudek, T. E. Tiwald, John A. Woollam

Department of Electrical and Computer Engineering: Faculty Publications

Silicon membranes are used for stencil masks which are key to charged particle projection lithography, particularly for ion projection lithography, electron beam projection. Quantitative and qualitative determination of the mechanical properties of the true thickness, thickness variations (morphology), electrical conductivity and stress is critical to the development of next generation lithography. The metrology setup includes high accuracy thickness, refractive index and electrical conductivity measurement based on infrared variable angle spectroscopic ellipsometry, thickness variation characterization based on the Fizeau interferometric scheme and mechanical stress evaluation based on a novel double bulging technique.

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Dc Power-Bus Modeling And Design With A Mixed-Potential Integral-Equation Formulation And Circuit Extraction, Jun Fan, James L. Drewniak, Hao Shi, James L. Knighten Nov 2001

Dc Power-Bus Modeling And Design With A Mixed-Potential Integral-Equation Formulation And Circuit Extraction, Jun Fan, James L. Drewniak, Hao Shi, James L. Knighten

Electrical and Computer Engineering Faculty Research & Creative Works

Application of a circuit extraction approach based on a mixed-potential integral equation formulation (CEMPIE) for dc power-bus modeling in high-speed digital designs is detailed herein. Agreement with measurements demonstrates the effectiveness of the approach. Dielectric losses are included into the calculation of Green's functions, and thus, incorporated into the rigorous first principles formulation. A SPICE model is then extracted from the discretized integral equation. A quasistatic approximation is used for Green's functions to keep the extracted circuit elements frequency independent. Previous work has established a necessary meshing criterion in order to ensure accuracy for a given substrate thickness and dielectric …

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Emi Mitigation With Multilayer Power-Bus Stacks And Via Stitching Of Reference Planes, Xiaoning Ye, David M. Hockanson, Min Li, Yong Ren, Wei Cui, James L. Drewniak, Richard E. Dubroff Nov 2001

Emi Mitigation With Multilayer Power-Bus Stacks And Via Stitching Of Reference Planes, Xiaoning Ye, David M. Hockanson, Min Li, Yong Ren, Wei Cui, James L. Drewniak, Richard E. Dubroff

Electrical and Computer Engineering Faculty Research & Creative Works

General methods for reducing printed circuit board (PCB) emissions over a broad band of high frequencies are necessary to meet EMI requirements, as processors become faster and more powerful. One mechanism by which EMI can be coupled off a PCB or multichip module (MCM) structure is from high-frequency fringing electric fields on the dc power and reference planes at the substrate periphery An approach for EMI mitigation by stitching multiple ground planes together along the periphery of multilayer PCB power-bus stacks with closely spaced vias is reported and quantified in this paper. Power-bus noise induced EMI and coupling from the …

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Stacked Subwavelength Gratings As Circular Polarization Filters, Gregory P. Nordin, P. C. Deguzman Nov 2001

Stacked Subwavelength Gratings As Circular Polarization Filters, Gregory P. Nordin, P. C. Deguzman

Faculty Publications

We have stacked subwavelength gratings (SWGs) on a single substrate to create a compact, integrated circular polarization filter. The SWGs consist of a wire grid polarizer and a broadband form-birefringent quarter-wave plate (QWP). Rigorous coupled-wave analysis was used to design the QWP for operation over the 3.5-5.0 m wavelength range. The fabricated silicon broadband QWP exhibited a phase retardance of 82-97° across this wavelength range. Two stacked structures are presented, each with a different wire grid polarizer fabricated on an organic planarization layer (SU-8) that is deposited on a QWP grating. Transmittance measurements of the first structure when illuminated with …

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Statistical Evaluation Of Image Quality Measures, Ismail Avcibas, Bulent Sankur, Khalid Sayood Oct 2001

Statistical Evaluation Of Image Quality Measures, Ismail Avcibas, Bulent Sankur, Khalid Sayood

Department of Electrical and Computer Engineering: Faculty Publications

In this work we comprehensively categorize image quality measures, extend measures defined for gray scale images to their multispectral case, and propose novel image quality measures. They are categorized into pixel difference-based, correlation-based, edge-based, spectral-based, context-based and human visual system (HVS)-based measures. Furthermore we compare these measures statistically for still image compression applications. The statistical behavior of the measures and their sensitivity to coding artifacts are investigated via analysis of variance techniques. Their similarities or differences are illustrated by plotting their Kohonen maps. Measures that give consistent scores across an image class and that are sensitive to coding artifacts are …

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Modeling And Test Of Pixel Cross-Talk In Hgcdte Focal Plane Arrays, Thomas J. Sanders, E. Lee Caraway, Glenn T. Hess, Gwendolyn W. Newsome, Theodore Fischer Oct 2001

Modeling And Test Of Pixel Cross-Talk In Hgcdte Focal Plane Arrays, Thomas J. Sanders, E. Lee Caraway, Glenn T. Hess, Gwendolyn W. Newsome, Theodore Fischer

Electrical Engineering and Computer Science Faculty Publications

Mercury Cadmium Telluride focal plane arrays with well over 1000 pixels have been fabricated for a number of years. These FPA's have been built as large two-dimensional arrays of HgCdTe p-n junction diodes on a single CdTe or CdZnTe substrate. Sensitivity of each pixel to impinging radiation is one of the most important quality factors for these devices. However, material parameters, which give diode high sensitivity, are the same as those that cause cross talk between adjacent diodes in the array. This cross talk causes a blurred image and in general is a detrimental factor for the FPA system. The …

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Detecting Novel Attacks By Identifying Anomalous Network Packet Headers, Philip K. Chan, Matthew V. Mahoney Oct 2001

Detecting Novel Attacks By Identifying Anomalous Network Packet Headers, Philip K. Chan, Matthew V. Mahoney

Electrical Engineering and Computer Science Faculty Publications

We describe a simple and efficient network intrusion detection algorithm that detects novel attacks by flagging anomalous field values in packet headers at the data link, network, and transport layers. In the 1999 DARPA off-line intrusion detection evaluation test set (Lippmann et. al. 2000), we detect 76% of probes and 48% of denial of service attacks (at 10 false alarms per day). When this system is merged with the 18 systems in the original evaluation, the average detection rate for attacks of all types increases from 61% to 65%. We investigate the effect on performance when attack free training data …

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Completeness Of Propositional Logic As A Program, Ryan Stansifer Oct 2001

Completeness Of Propositional Logic As A Program, Ryan Stansifer

Electrical Engineering and Computer Science Faculty Publications

The proof of completeness for propositional logic is a constructive one, so a computer program is suggested by the proof. We prove the completeness theorem for Łukasiewicz’ axioms directly, and translate the proof into the functional languages SML and Haskell. In this paper we consider this proof as a program. The program produces enormous proof trees, but it is, we contend, as good a proof of completeness as the standard mathematical proofs.The real value of the exercise is the further evidence it provides that typed, functional languages can clearly express the complex abstractions of mathematics.

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