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BME 331 Biosignals and Systems

Course description:

BME 331 is a combined lecture and laboratory course in signals and systems analysis for Biomedical Engineering students in the first semester of their junior year. The theory is introduced from a decidedly biological perspective with analytical training to include: time and frequency domain analysis of continuous and discrete systems, c ontinuous and discrete Fourier series and transforms, representation of discrete systems using difference equations and Z-transforms, state equations, feedback and system stability.

Prerequisites:

Math 261, Math 262, Biology K101, Physics 251, BME 211 & proficiency in MATLAB and LabVIEW.

Corequisites:

Biology K324

Instructional Goals:

This course provides the foundational skills for the mathematical representation and analysis of biological signals. The b asic analytical concepts for modeling and analysis of biological system dynamics are also mastered. All computational homework assignments are carried out using MATLAB. All laboratory exercises are carried out using LabVIEW.

Required Textbook:

Biomedical Signal Processing and Signal Modeling by Eugene N. Bruce (2001), Wiley Interscience. ISBN: 0-471-34540-7. Both electronic and printed handouts will also be distributed throughout the semester.

Additional reference materials:

1. Cooper, GR & McGillem, CD: Probabilistic Methods of signal and System Analysis, fourth edition or earlier, Oxford . ISBN: 0-190512354-9
2. Kandel, ER & Schwartz, JH: Principles of Neuroscience. Second through fourth editions, Elsevier. ISBN: 0838577016
3. Berne , RM (Editor), Levy, MN, Koeppen, BM & Stanton: Physiology. Fourth edition, Mosby, ISBN: 0815109520
4. Bronzino, JD (Editor), The Biomedical Engineering Handbook, CRC Press, ISBN 0849383463

General Lecture Topics:

BME 331 is comprised of three interrelated subject areas, all involving the use of mathematical and computational tools to extract meaningful information from biological signals and systems. The first subject area broadly introduces the topic of biological systems that rely on negative feedback for control and stability. Classical concepts of feedback system analysis and associated compensation techniques are introduced using root locus, Bode diagram, and Nyquist criterion as determinants of stability. The second subject area broadly introduces the topic of biological signals as an electrical event. Standard analytical methods of signal representation such as Fourier analysis and power spectrum are developed in order to quantify the information content of these biological signals. The third subject area utilizes recent articles from the scientific literature demonstrating the application of these and other mathematical processing techniques in the study of biological signals and physiological systems. Refer to the lecture schedule for specific topics and dates.

Outcomes:

Upon completion of the course, students should be able to

•  Determine the Fourier and Z transforms of continuous and discrete signals and systems, and determine the state transition matrices for linear dynamic systems to study the dynamic responses [a]
•  Determine the conditions and study the stability of systems and convergence of signals (continuous- and discrete-time). [b1, b2]
•  Determine and apply the appropriate methods and techniques to study transient responses and stability after determining the nature of the signals and systems [a]
•  Determine the output of continuous and discrete-time filters for input signals of different magnitude and frequency. [a, b2, c]
•  Determine the applicability of different methods (e.g., Laplace transform, continuous and discrete-time, etc.) for linear and nonlinear dynamic systems with applications to the analysis of stability and dynamic responses of biological systems [a]