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Full-Text Articles in Engineering

Observer Incorporated Neoclassical Controller Design: A Discrete Perspective, Winston Alexander Baker Aug 2010

Observer Incorporated Neoclassical Controller Design: A Discrete Perspective, Winston Alexander Baker

Master's Theses (2009 -)

Control theory has generally been divided into two categories, modern control and classical control. Modern control uses state feedback to alter the pole locations of a given system. Classical control uses pre-compensation to alter the zeroes of the system and uses output feedback to adjust the poles to bring stability to the system. The drawback is that the application of classical control techniques can be a lengthy, complicated and iterative design process and in the end, classical control techniques still do not give information about the state of the system. Neoclassical control combines classical control techniques with the state feedback …


Effect Of Magnetron Frequency On Heating Pattern In Domestic Oven, Sohan Birla, Krishnamoorthy Pitchai, Jeyamkondan Subbiah, David D. Jones Jan 2010

Effect Of Magnetron Frequency On Heating Pattern In Domestic Oven, Sohan Birla, Krishnamoorthy Pitchai, Jeyamkondan Subbiah, David D. Jones

Department of Biological Systems Engineering: Conference Presentations and White Papers

In this study a computer model was developed to simulate microwave heating of a model food with a range of magnetron frequencies. The range was decided upon performing the frequency spectrum analysis of microwave leakage from the microwave oven. Simulation results showed that the magnetron input as sinusoidal frequency from 2.44 GHz to 2.48 GHz generates different heating profiles. The simulated heating profiles were compared with experimental heating profiles obtained by using an IR camera. None of simulations with individual frequency exactly matches with experimental temperature profile. The closet match between simulated and observed temperature profiles was found with 2.46 …


Unified Large And Small Signal State-Space Based Modeling And Symbolic Simulation For Pwm Converters, Ehab Shoubaki Jan 2009

Unified Large And Small Signal State-Space Based Modeling And Symbolic Simulation For Pwm Converters, Ehab Shoubaki

Electronic Theses and Dissertations

In this Dissertation, which concentrates on discrete modeling for control purposes of DC/DC converters and simulation through symbolic techniques. A Unified Discrete State-Space Model for power converters in CCM is presented. Two main approaches to arriving at the discrete model are used. The first approach involves an impulse function approximation of the duty cycle modulation of the converter switches, and this approach results in a small signal discrete model. The Second approach is direct and does not involve any approximation of the modulation, this approach yields both a large signal nonlinear discrete model and a linear small signal model. Harmonic …


High Voltage Dc Converter Systems Modeling, Simulation And Analysis, Manish A. Dalal Jan 2009

High Voltage Dc Converter Systems Modeling, Simulation And Analysis, Manish A. Dalal

Browse all Theses and Dissertations

The thesis provides insights into important modeling techniques to model the converter system, machine design, control and power stages and integration of the various sub systems to simulate the system level performance. This innovative modeling and simulation project is very relevant to optimizing the system performance, designing the sub circuits, components selection, predicting the system stability and impulse responses. The thesis presents modeling and simulation of three different 270VDC converter systems and comparing their performances against each other. The 270VDC converter system accepts either Generator 3-phase AC voltages or fixed three voltage source followed by single or dual converter stages …


Real-Time Implementation Of Intelligent Modeling And Control Techniques On A Plc Platform, Curtis Alan Parrott, Ganesh K. Venayagamoorthy Oct 2008

Real-Time Implementation Of Intelligent Modeling And Control Techniques On A Plc Platform, Curtis Alan Parrott, Ganesh K. Venayagamoorthy

Electrical and Computer Engineering Faculty Research & Creative Works

Programmable logic controllers (PLCs) have been used for many decades for standard control in industrial and factory environments. Over the years, PLCs have become computational efficient and powerful, and a robust platform with applications beyond the standard control and factory automation. Due to the new advanced PLC's features and computational power, they are ideal platforms for exploring advanced modeling and control methods, including computational intelligence based techniques such as neural networks, particle swarm optimization (PSO) and many others. Some of these techniques require fast floating-point calculations that are now possible in real-time on the PLC. This paper focuses on the …


Development And Validation Of A Microcontroller Model For Emc, Shaohua Li, Hemant Bishnoi, Jason Whiles, Pius Ng, Haixiao Weng, David Pommerenke, Daryl G. Beetner Sep 2008

Development And Validation Of A Microcontroller Model For Emc, Shaohua Li, Hemant Bishnoi, Jason Whiles, Pius Ng, Haixiao Weng, David Pommerenke, Daryl G. Beetner

Electrical and Computer Engineering Faculty Research & Creative Works

Models of integrated circuits (ICs) allow printed circuit board (PCB) developers to predict radiated and conducted emissions early in board development and allow IC manufactures insight into how to build their ICs better for electromagnetic compatibility (EMC). A model of the power delivery network, similar to the ICEM or LECCS model, was developed for a microcontroller running a typical program and used to predict the noise voltage between the power and return planes of a PCB. The IC and package model was generated using the Apache tool suite. A model of the PCB was created using an electromagnetic cavity model …


Estimation Of The Statistical Variation Of Crosstalk In Wiring Harnesses, Meilin Wu, Daryl G. Beetner, Todd H. Hubing, Haixin Ke, Shishuang Sun Aug 2008

Estimation Of The Statistical Variation Of Crosstalk In Wiring Harnesses, Meilin Wu, Daryl G. Beetner, Todd H. Hubing, Haixin Ke, Shishuang Sun

Electrical and Computer Engineering Faculty Research & Creative Works

Analyzing interference problems in vehicle wiring harnesses requires fast and accurate methods of approximating crosstalk. Worst-case approximations using lumped element models are fast and easy to use, but run the risk of overestimating problems. Statistical methods that account for the random variation of wire position help prevent overdesign, but are often difficult and time-consuming to apply and lack a clear link between problems and their cause. Here we investigate the use of simple lumped-element models to predict the statistical variation of crosstalk in wire harness bundles. Models are based on lumped-element approximations, where inductance and capacitance values are calculated for …


Modeling Of Liquid Crystal Display And Photonic Devices, Zhibing Ge Jan 2007

Modeling Of Liquid Crystal Display And Photonic Devices, Zhibing Ge

Electronic Theses and Dissertations

Liquid crystal (LC) materials have been widely applied in electro-optical devices, among which display is the most successful playground and numerous new applications in photonic areas (such as laser beam steering devices) are also emerging. To well guide the device design for optimum performance, accurate modeling is of prior and practical importance. Generally, the modeling of LC devices includes two parts in sequence: accurate LC molecule deformation extraction under external electric fields and optical calculation thereafter for the corresponding electro-optical behaviors. In this dissertation, first, hybrid finite element method and finite difference method are developed to minimize the free energy …


Four Terminal Junction Field-Effect Transistor Model For Computer-Aided Design, Hao Ding Jan 2007

Four Terminal Junction Field-Effect Transistor Model For Computer-Aided Design, Hao Ding

Electronic Theses and Dissertations

A compact model for four-terminal (independent top and bottom gates) junction field-effect transistor (JFET) is presented in this dissertation. The model describes the steady-state characteristics with a unified equation for all bias conditions that provides a high degree of accuracy and continuity of conductance, which are important for predictive analog circuit simulations. It also includes capacitance and leakage equations. A special capacitance drop-off phenomenon at the pinch-off region is studies and modeled. The operations of the junction fieldeffect transistor (JFET) with an oxide top-gate and full oxide isolation are analyzed, and a semi-physical compact model is developed. The effects of …


Validation Of Worst-Case And Statistical Models For An Automotive Emc Expert System, Daryl G. Beetner, Haixiao Weng, Meilin Wu, Todd H. Hubing Jan 2007

Validation Of Worst-Case And Statistical Models For An Automotive Emc Expert System, Daryl G. Beetner, Haixiao Weng, Meilin Wu, Todd H. Hubing

Electrical and Computer Engineering Faculty Research & Creative Works

Previous papers have presented algorithms for an EMC expert system used to predict potential electromagnetic compatibility problems in a vehicle early in the design process. Here, the accuracy of inductive and capacitive coupling algorithms are verified through representative measurements of crosstalk within an automobile. Worst-case estimates used by the algorithms are compared to measured values and are compared to values estimated using statistical methods. The worst-case algorithms performed well up to 10-20 MHz, but overestimated measured results by several dB in some cases and up to 10-15 dB in others. An approximate statistical variation of the current expert system algorithms …


Predicting Tem Cell Measurements From Near Field Scan Data, Haixiao Weng, Daryl G. Beetner, Richard E. Dubroff Aug 2006

Predicting Tem Cell Measurements From Near Field Scan Data, Haixiao Weng, Daryl G. Beetner, Richard E. Dubroff

Electrical and Computer Engineering Faculty Research & Creative Works

A procedure is proposed for predicting TEM cell measurements from near field scans by modeling near-field scan data using equivalent sources. The first step in this procedure is to measure the tangential electric and magnetic fields over the circuit. Electric and magnetic fields are estimated from probe measurements by compensating for the characteristics of the probe. An equivalent magnetic and electric current model representing emissions is then generated from the compensated fields. These equivalent sources are used as an impressed source in an analytical formula or full wave simulation to predict measurements within the TEM cell. Experimental verification of the …


Simulation And Modeling Of Return Waveforms From A Ladar Beam Footprint In Usu Ladarsim, Scott E. Budge, B.C. Leishman, R.T. Pack May 2006

Simulation And Modeling Of Return Waveforms From A Ladar Beam Footprint In Usu Ladarsim, Scott E. Budge, B.C. Leishman, R.T. Pack

Electrical and Computer Engineering Faculty Publications

Ladar systems are an emerging technology with applications in many fields. Consequently, simulations for these systems have become a valuable tool in the improvement of existing systems and the development of new ones. This paper discusses the theory and issues involved in reliably modeling the return waveform of a ladar beam footprint in the Utah State University LadarSIM simulation software. Emphasis is placed on modeling system-level effects that allow an investigation of engineering tradeoffs in preliminary designs, and validation of behaviors in fabricated designs. Efforts have been made to decrease the necessary computation time while still maintaining a usable model. …


Characterization Of Transmission Lines At Ir, Tasneem A. Mandviwala, José Manuel López-Alonso, Brian A. Lail, Glenn D. Boreman May 2006

Characterization Of Transmission Lines At Ir, Tasneem A. Mandviwala, José Manuel López-Alonso, Brian A. Lail, Glenn D. Boreman

Electrical Engineering and Computer Science Faculty Publications

We demonstrate the first long wave infrared (LWIR) transmission line design and characterization. Two of the widely used transmission-lines: coplanar striplines (CPS) and microstrip (MS) lines are characterized at IR frequency (28.3THz), in terms of transmission line parameters: characteristic impedance (Z₀, attenuation constant (α) and effective index of refraction (nᵉᶠᶠ), through modeling, fabrication and measurement. These transmission-line parameters cannot be directly measured, what can be measured is the antenna response. So we compute, measure and compare the response of the dipole antenna connected to these transmission lines as a function of transmission-line length. The response depends on the transformation of …


Study Of Nanoscale Cmos Device And Circuit Reliability, Chuanzhao Yu Jan 2006

Study Of Nanoscale Cmos Device And Circuit Reliability, Chuanzhao Yu

Electronic Theses and Dissertations

The development of semiconductor technology has led to the significant scaling of the transistor dimensions -The transistor gate length drops down to tens of nanometers and the gate oxide thickness to 1 nm. In the future several years, the deep submicron devices will dominate the semiconductor industry for the high transistor density and the corresponding performance enhancement. For these devices, the reliability issues are the first concern for the commercialization. The major reliability issues caused by voltage and/or temperature stress are gate oxide breakdown (BD), hot carrier effects (HCs), and negative bias temperature instability (NBTI). They become even more important …


Circuit Models For Power Bus Structures On Printed Circuit Boards Using A Hybrid Fem-Spice Method, Todd H. Hubing, Chunlei Guo Jan 2006

Circuit Models For Power Bus Structures On Printed Circuit Boards Using A Hybrid Fem-Spice Method, Todd H. Hubing, Chunlei Guo

Electrical and Computer Engineering Faculty Research & Creative Works

Power bus structures consisting of two parallel conducting planes are widely used on high-speed printed circuit boards. In this paper, a full-wave finite-element method (FEM) method is used to analyze power bus structures, and the resulting matrix equations are converted to equivalent circuits that can be analyzed using SPICE programs. Using this method of combining FEM and SPICE, power bus structures of arbitrary shape can be modeled efficiently both in the time-domain and frequency-domain, along with the circuit components connected to the bus. Dielectric loss and losses due to the finite resistance of the power planes can also be modeled. …


Simulation Model For Assessing Transient Performance Of Capacitive Voltage Transformers, I. Sule, Ganesh K. Venayagamoorthy, U. O. Aliyu Jan 2006

Simulation Model For Assessing Transient Performance Of Capacitive Voltage Transformers, I. Sule, Ganesh K. Venayagamoorthy, U. O. Aliyu

Electrical and Computer Engineering Faculty Research & Creative Works

In determining the correct operation of relays of a protection scheme, proper representation of instrument transformers and their behavior in conditions where there can be transient is very critical. This paper presents a simulation model for assessing the transient performance of capacitive voltage transformers (CVTs). In order to test the validity of the developed model, four CVT operational conditions are considered using field data collected from one of the Nigerian electric utility 330/132/33 kV substations. The model simulation results revealed various configuration performance responses that could affect relay protection schemes to different degrees. As expected, the CVT responses showed that …


A Synchronous Primary-Side Dimming Controller For Cold-Cathode Fluorescent Lamp Ballast, Jenn-Jong Shieh Jun 2005

A Synchronous Primary-Side Dimming Controller For Cold-Cathode Fluorescent Lamp Ballast, Jenn-Jong Shieh

Journal of Marine Science and Technology

In this paper, a rectified quasi-sinusoidal pulse width modulation (RQSPWM) controller is first proposed for the cold-cathode fluorescent lamp (CCFL) ballast to achieve a synchronous primary-side dimming control. It is seen that, with the novel controller, not only the lamp flickering problem and the thermometer effect can be eliminated but also the useful photo-coupler in secondary side can be avoided to reduce cost. Then, small signal models of the CCFL ballast and the proposed RQSPWM dimming controller are derived to analyze the performance of the ballast system and help corroborate hardware loop measurements. Finally, a prototype is constructed for verifying …


Modeling And Simulation Of Long Term Degradation And Lifetime Of Deep-Submicron Mos Device And Circuit, Zhi Cui Jan 2005

Modeling And Simulation Of Long Term Degradation And Lifetime Of Deep-Submicron Mos Device And Circuit, Zhi Cui

Electronic Theses and Dissertations

Long-term hot-carrier induced degradation of MOS devices has become more severe as the device size continues to scale down to submicron range. In our work, a simple yet effective method has been developed to provide the degradation laws with a better predictability. The method can be easily augmented into any of the existing degradation laws without requiring additional algorithm. With more accurate extrapolation method, we present a direct and accurate approach to modeling empirically the 0.18-ìm MOS reliability, which can predict the MOS lifetime as a function of drain voltage and channel length. With the further study on physical mechanism …


A Microphone Array System For Multimedia Applications With Near-Field Signal Targets, Y. Rosa Zheng, M. El-Tanany, R. A. Goubran, Hongchi Shi Jan 2005

A Microphone Array System For Multimedia Applications With Near-Field Signal Targets, Y. Rosa Zheng, M. El-Tanany, R. A. Goubran, Hongchi Shi

Electrical and Computer Engineering Faculty Research & Creative Works

A microphone array beamforming system is proposed for multimedia communication applications using four sets of small planar arrays mounted on a computer monitor. A new virtual array approach is employed such that the original signals received by the array elements are weighted and delayed to synthesize a large, nonuniformly spaced, harmonically nested virtual array covering the frequency band [50, 7000] Hz of the wideband telephony. Subband multirate processing and near-field beamforming techniques are then used jointly by the nested virtual array to improve the performances in reverberant environments. A new beamforming algorithm is also proposed using a broadband near-field spherically …


Electromagnetic Interference (Emi) Of System-On-Package (Sop), Toshio Sudo, Hideki Sasaki, Norio Masuda, James L. Drewniak May 2004

Electromagnetic Interference (Emi) Of System-On-Package (Sop), Toshio Sudo, Hideki Sasaki, Norio Masuda, James L. Drewniak

Electrical and Computer Engineering Faculty Research & Creative Works

Electromagnetic interference (EMI) issues are expected to be crucial for next-generation system-on-package (SOP) integrated high-performance digital LSIs and for radio frequency (RF) and analog circuits. Ordinarily in SOPs, high-performance digital LSIs are sources of EMI, while RF and analog circuits are affected by EMI (victims). This paper describes the following aspects of EMI in SOPs: 1) die/package-level EMI; 2) substrate-level EMI; 3) electromagnetic modeling and simulation; and 4) near electromagnetic field measurement. First, LSI designs are discussed with regard to radiated emission. The signal-return path loop and switching current in the power/ground line are inherent sources of EMI. The EMI …


Hgcdte Focal Plane Array Cost Modeling, Thomas J. Sanders, Glenn T. Hess Oct 2003

Hgcdte Focal Plane Array Cost Modeling, Thomas J. Sanders, Glenn T. Hess

Electrical Engineering and Computer Science Faculty Publications

Focal plane arrays (FPAs) are used in many applications for detecting infrared (IR) radiation where normal sight with light in the visible spectrum is not possible. To effectively detect this IR radiation, complex semiconductor diodes, cooled to low temperatures, are usually used. The most common of these semiconductor materials is the II-VI alloy semiconductor system using HgCdTe, which is often called MCT. Focal plane arrays with over 1000 pixels have been fabricated. The cost of these very complex systems is becoming a very important consideration in decisions of where to use these FPAs. The focal plane array actually consists of …


Channel Probing For An Indoor Wireless Communications Channel, Brandon Hunter Mar 2003

Channel Probing For An Indoor Wireless Communications Channel, Brandon Hunter

Theses and Dissertations

The statistics of the amplitude, time and angle of arrival of multipaths in an indoor environment are all necessary components of multipath models used to simulate the performance of spatial diversity in receive antenna configurations. The model presented by Saleh and Valenzuela, was added to by Spencer et. al., and included all three of these parameters for a 7 GHz channel. A system was built to measure these multipath parameters at 2.4 GHz for multiple locations in an indoor environment. Another system was built to measure the angle of transmission for a 6 GHz channel. The addition of this parameter …


Steady State Simulation Of Ysz Intermediate-Temperature Fuel Cell, Zi-Jing Lin, Ye Gu, Xiao-Hua Zhang Nov 2002

Steady State Simulation Of Ysz Intermediate-Temperature Fuel Cell, Zi-Jing Lin, Ye Gu, Xiao-Hua Zhang

Journal of Electrochemistry

With a coupled 2D electrochemical and thermal modeling software, the characteristics of the steady state operation of the intermediate-temperature fuel cell with thin yttria-stabilized zirconia(YSZ) electrolyte was analyzed. The parameters of I-V equation were obtained from fitting the experiment results and the choice of grid points was determined by balancing the accuracy requirement and computational efficiency. The temperature fields at different operation circumstances such as flow designs, material choices for interconnect, were examined. The dependences of the output power and cell efficiency on the operating voltage at different temperatures were studied. Based upon the analysis of the temperature profile, it …


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 …


Emi Model Validation And Standard Challenge Problems, Bruce Archambeault, James L. Drewniak Mar 2000

Emi Model Validation And Standard Challenge Problems, Bruce Archambeault, James L. Drewniak

Electrical and Computer Engineering Faculty Research & Creative Works

A joint effort of the IEEE/EMC Society TC-9 Committee and the Applied Computational Electromagnetic Society (ACES) resulted in a central web location for contributors who will provide model and measurement data to share and compare with others. In addition to the data repository, a set of standard challenge problems have been proposed over the past few years, and are located at the web site. The site will be carefully monitored by a review committee to insure only high-quality information is posted on the site.


Incorporating Vertical Discontinuities In Power-Bus Modeling Using A Mixed-Potential Integral Equation And Circuit Extraction Formulation, Jun Fan, Hao Shi, James L. Drewniak, Todd H. Hubing, Richard E. Dubroff, Thomas Van Doren Oct 1998

Incorporating Vertical Discontinuities In Power-Bus Modeling Using A Mixed-Potential Integral Equation And Circuit Extraction Formulation, Jun Fan, Hao Shi, James L. Drewniak, Todd H. Hubing, Richard E. Dubroff, Thomas Van Doren

Electrical and Computer Engineering Faculty Research & Creative Works

Noise on the DC power-bus attributed to device switching is among the primary sources of EMI and signal integrity problems. A mixed-potential integral equation formulation with circuit extraction approach is used to model the planar multi-layer power-bus geometry, which can also include arbitrary shaped power regions on multiple layers. Incorporating vertical discontinuities, e.g., decoupling capacitor interconnects, is a critical aspect of the modeling, and must be done properly since they are included as a lumped element model and not a part of the MPIE formulation. Agreement with experimental results demonstrate the present approach.


Design, Modeling, And Characterization Of Fet-Seed Smart Pixel Transceiver Arrays For Optical Backplanes, David V. Plant, Alain Z. Shang, Marcos R. Otazo, David R. Rolston, Brian Robertson, Harvard Scott Hinton Jan 1996

Design, Modeling, And Characterization Of Fet-Seed Smart Pixel Transceiver Arrays For Optical Backplanes, David V. Plant, Alain Z. Shang, Marcos R. Otazo, David R. Rolston, Brian Robertson, Harvard Scott Hinton

Electrical and Computer Engineering Faculty Publications

The design, modeling, and characterization of FET-SEED smart pixel transceiver arrays fabricated for application in optical backplanes are presented. Results of digital and analog measurements on 4×4 transmitter arrays and 4×4 receiver arrays, packaged at the printed circuit-board level, will be presented. In addition, these results will be compared to device and circuit models developed for these optoelectronics. Finally, the description of the successful application of these optoelectronics to interconnect two printed circuit boards will be described.


Diagnosing And Modeling Common-Mode Radiation From Printed Circuit Boards With Attached Cables, James L. Drewniak, Fei Sha, Todd H. Hubing, Thomas Van Doren, J. Shaw Aug 1995

Diagnosing And Modeling Common-Mode Radiation From Printed Circuit Boards With Attached Cables, James L. Drewniak, Fei Sha, Todd H. Hubing, Thomas Van Doren, J. Shaw

Electrical and Computer Engineering Faculty Research & Creative Works

A procedure for diagnosing and modeling radiation from printed circuit boards with attached cables is presented through a case study of a production model electronic control unit. Procedures for determining EMI antennas, IC sources, and mechanisms by which noise is coupled from the IC source to the antenna are suggested.


Modeling Power Bus Decoupling On Multilayer Printed Circuit Boards, James L. Drewniak, Todd H. Hubing, Thomas Van Doren, P. Baudendistal Aug 1994

Modeling Power Bus Decoupling On Multilayer Printed Circuit Boards, James L. Drewniak, Todd H. Hubing, Thomas Van Doren, P. Baudendistal

Electrical and Computer Engineering Faculty Research & Creative Works

Power bus decoupling designs on multilayer printed circuit boards must adequately account for the power bus interplane capacitance and its consequences for the design. Lumped element models for a power bus on a multilayer printed circuit board where an appreciable or entire portion of a layer is devoted to power and ground have been developed. The models are applicable below the distributed resonances of the board. Analytical, circuit simulation, and experimental studies have been conducted to test the models, investigate the effects of the distributed interplane capacitance of the power bus, and the effect of interconnect inductance associated with surface-mount …


A Method Of Modeling Multirate Two-Dimensional Recursive Digital Filters Author, Albert P. Gerheim Apr 1981

A Method Of Modeling Multirate Two-Dimensional Recursive Digital Filters Author, Albert P. Gerheim

Electrical & Computer Engineering Theses & Dissertations

This dissertation presents a method of modeling two dimensional sampled data systems with two sampling rates in each dimension. This methodology is applied to the problem of synthesizing two dimensional velocity filters using one dimensional prototypes and multirate concepts.

The modeling method includes the replacement of scalar z-transforms of signals by vectors of polynomials, and the replacement of scalar z-transforms of impulse responses by matrices of polynomials.

The synthesis of velocity filters is accomplished through the use of coordinate transformations in the z-transform domain which skew the ω12 axes on the unit bidisc. The filters synthesized using …