Joseph P. Hoffbeck

A method for estimating the number of components in a normal mixture density function

A criticism of using the Gaussian density function to model the classes in multispectral remote sensing data is that the classes may be multimodal, and therefore, not well represented by the Gaussian density function. The normal mixture density function, which is the sum of one or more weighted Gaussian components, is a compromise between Gaussian and non-parametric density functions. It can model multimodal density functions, yet requires fewer parameters to be estimated than non-parametric density functions, which is an advantage in remote sensing applications where training samples are difficult and expensive to obtain. Usually in practice, the number of components is not known, and must be estimated from the training samples. A new approach for estimating the appropriate number of components in a normal mixture density is described. The approach is to divide the data from each class into various numbers of clusters using the nearest means algorithm, compute a measure of fit which measures how well the training data are represented by the clusters, and to select the number of clusters that best fits the data. The measure of fit is computed by leaving one sample out and estimating the mean vectors and covariance matrices of the mixture density with the rest of the samples. Then the likelihood of the left-out sample is computed, and the process is repeated, each time leaving out a different sample. In this way, the samples used to test the estimates are independent of the samples used to compute estimates, and so the measure of fit, which is the average log likelihood of the left-out samples, does not increase monotonically like the joint likelihood, but will reach a maximum. The number of clusters that results in the maximum value of the measure of fit is selected as the estimate of the number of components in the mixture density.

Discovering the effects of feedback on control systems: informative and interesting numerical exercises

A numerical approach to feedback investigations allows students to discover easily and quickly the basic effects of feedback, both desirable and undesirable, on automatic control systems. Students can quickly learn the intuitive aspects of feedback early in their study of control systems before they enter, and perhaps become lost in, the world of intense mathematical analysis and design applied to feedback. The illustrative example presented in this paper, which is designed to match the preferred learning style of most engineering students, can be used to form coordinated numerical and analytical exercises in lecture, recitation, or laboratory portions of the course. Our students say that they enjoy and benefit from the many learning aspects of these discovery exercises.

Interfacing MATLAB with a parallel virtual processor for matrix algorithms

Abstract This paper describes the results of a project to interface MATLAB with a parallel virtual processor (PVP) that allows execution of matrix operations in MATLAB on a set of computers connected by a network. The software, a connection-oriented BSD socket-based client–server model, automatically partitions a MATLAB problem and delegates work to server processes running on separate remote machines. Experimental data on the matrix multiply operation shows that the speed improvement of the parallel implementation over the single-processor MATLAB algorithm depends on the size of the matrices, the number of processes, the speed of the processors, and the speed of the network connection. In particular, the advantage of doing matrix multiply in parallel increases as the size of the matrices increase. A speedup of 2.95 times was achieved in multiplying 2048 by 2048 square matrices using 15 workstations. The algorithm was also implemented on a network of four PCs, which was up to 2.5 times as fast as four workstations. The study also showed that there is an optimal number of processes for a particular problem, and so using more processes is not always faster.

Real-time FM radio for teaching DSP and communication systems

In digital signal processing (DSP) and communication systems courses much of the material is theoretical. There are some students who are more motivated to learn if they can see a connection to the real world, but unfortunately many real-world communication and DSP systems are very complex, and including them as part of a course is difficult or impossible. The FM radio, however, is a relatively simple system that is in some ways ideal as a real-world example because it includes both analog and digital signals. The analog signals transmit the audio and the digital Radio Data System (RDS) signal transmits auxiliary information such as the name of the artist, song, current time, etc. This paper describes an FM radio with RDS decoder based on an inexpensive FM module and an affordable DSP board. The system runs in real-time, demodulates FM radio, plays the music through speakers, displays the name of the song and artist, and allows access to the internal signals. This real-time receiver can be used in demonstrations in a lecture course or as the basis for a series of laboratory experiments.

Design of a Power Waveform Capture Platform for Plug Load Monitoring

Plug loads in consumer electronic products consume large quantities of energy, often without the knowledge of the user. To facilitate the development of smart plug strips and new building control systems, an open-source power waveform capture platform has been designed and tested. The system was developed to accurately and safely record the voltage and current waveforms for any plug load such as consumer electronic and electrical systems. The device incorporates a commercially available hardware platform that has been reprogrammed to record the voltage and current waveforms and transfer them in real-time to a computer for storage and further processing. The system samples the voltage and current waveforms with a sampling rate of 2048 Hz, and this detailed data can be used to identify the types of waveforms that are associated with various devices, as well as measure any power parameter of interest such as real power, energy, RMS volts, RMS current, power factor, frequency, etc. The system has been tested with several known electrical loads and has been found to perform well. The paper describes the hardware and software, the test setup, and the test results. Since the hardware is inexpensive (about

Classification of high dimensional multispectral data

250) and the software is available for free from the authors, this system can be used by almost anyone to perform detailed studies of the power characteristics of electrical and electronic devices.Copyright