BMDE 519 - Outline_Introduction

BMDE 519 - Outline_Introduction - B MDE: 519 ANALYSIS OF...

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Unformatted text preview: B MDE: 519 ANALYSIS OF BIOMEDICAL SIGNALS AND SYSTEMS COURSE OUTLINE & INFORMATION, SEPTEMBER 2009 ROBERT.KEARNEY@MCGILL.CA Objectives ...................................................................................................................................................................... 1 Outline ........................................................................................................................................................................... 2 1) Basic Tools & Concepts ..................................................................................................................................... 2 2) Amplitude Structure Of Signals ........................................................................................................................ 2 3) Frequency Content Of Signals .......................................................................................................................... 2 4) Filtering ............................................................................................................................................................. 2 5) Sampling Considerations .................................................................................................................................. 2 6) Correlation Functions ....................................................................................................................................... 2 7) Introduction to Systems Analysis ..................................................................................................................... 2 8) The Method of Least Squares ........................................................................................................................... 2 9) Impulse Response Functions ............................................................................................................................ 2 10) Frequency Response Analysis ........................................................................................................................... 2 Time ............................................................................................................................................................................... 3 Teaching Methods ......................................................................................................................................................... 3 Teaching Assistant ......................................................................................................................................................... 3 Communication ............................................................................................................................................................. 3 Evaluation ...................................................................................................................................................................... 3 WebCT ........................................................................................................................................................................... 4 MATLAB ......................................................................................................................................................................... 4 Academic Integrity ......................................................................................................................................................... 5 OBJECTIVES The objective of the course is to familiarize students with basic techniques for the quantitative analysis of biomedical systems and signals. Particular emphasis will be placed on methods appropriate to the biomedical research environment. The theoretical background for each technique will be presented briefly, but the major stress will be on practical application of the methods and interpretation of results. This will be achieved by having students undertake assignments involving the analysis of simulated and actual biomedical data. 1 September 2009 1/5 B MDE: 519 ANALYSIS OF BIOMEDICAL SIGNALS AND SYSTEMS 6) C ORRELATION FUNCTIONS OUTLINE 1) B ASIC TOOLS & CONCEPTS Signals & systems; deterministic and random variables; probability distributions; realizations; stationary & nonstationary processes; ergodicity; properties of random signals; estimators; amplitude statistics; correlation & covariance; linear function of random variables 2) A MPLITUDE STRUCTURE OF SIGNALS Probability distributions, probability densities, joint probability distributions; statistical independence; Gaussian distribution and its properties; other distributions; amplitude histograms; identification of distributions 3) F REQUENCY CONTENT OF SIGNALS Periodic signals; Fourier series; discrete Fourier spectra; the Fourier transform; power spectra 4) F ILTERING Auto‐correlation, auto‐covariance, and auto‐ correlation coefficient functions; cross‐correlation, cross‐covariance, and cross‐correlation coefficient functions; estimation of correlation functions; relation between correlation functions and spectral densities; practical applications 7) I NTRODUCTION ANALYSIS TO SYSTEMS Static and dynamic systems; time‐varying and time invariant systems; mathematical modeling; linear systems, superposition and proportionality; importance of linearity; testing for linearity; linear range; Laplace transforms; transfer functions 8) T HE METHOD OF LEAST SQUARES Linear statistical models; the least squares problem; matrix formulation of least squares; properties of least squares estimates; comparing models; total least squares; non‐linear minimization 9) I MPULSE RESPONSE FUNCTIONS Types of noise; low‐pass, band‐pass, high‐pass and band‐reject filters; Bode plots; cut‐off frequency and roll‐off; analog filters; digital filters: frequency domain implementations, FIR filters, recursive filters 5) S AMPLING CONSIDERATIONS Digitization, sampling, and quantization; Shannon‐ Nyquist sampling theorem; aliasing; Nyquist frequency; quantization; quantization theorem; analog‐digital converters; digital‐analog converters Impulse response functions (IRF); convolution; parametric vs. nonparametric IRF; IRF determination 10) FREQUENCY RESPONSE ANALYSIS Frequency response; sinusoidal frequency response determination; stochastic frequency response determination; practical applications 1 September 2009 2/5 BMDE: 519 ANALYSIS OF BIOMEDICAL SIGNALS AND SYSTEMS Outline & Information He will TIME 1. Monitor the WebCT discussion board, provide first‐level help. 3. Wednesday. September 9, 2008 Room 321, Lyman Duff Medical Sciences Building, 3775 University Mark all assignments. 2. The class meets Wednesdays from 16:00‐18:00. The first meeting will be: Attend all classes, provide a summary of the problems encountered in the most recent assignments, and answer any questions regarding individual marks. TEACHING METHODS COMMUNICATION The course will be given in three main components: modules, assignments, and lectures. Modules, each covering a particular topic, and containing a summary of important background material, references to further reading, illustrative examples, and an assignment. Classes are intended to be tutorial in nature and so the best time to ask questions will be during class. Assignments are the most important part of the course; they will be used to stress and develop further the points made in the background material, demonstrate the applicability, strengths and limitations of particular methods, and test understanding of material. The preferred method of communication out of class will be the WebCT discussion group. If you have questions regarding course material it is most likely that others will as well. By posting the questions on the discussion group others will benefit. Questions of an individual nature, or request for meetings, should be sent by e‐ mail to the instructor or TA using their McGill e‐mail address. Lectures will be informal. Some time will be devoted to introducing the new material in each week’s module. However, the majority of each session will be devoted to a tutorial discussion and review of material from previous modules. The value of the tutorial (and its length) will depend largely upon the degree of student involvement. EVALUATION Students will be evaluated on their term work, as evidenced by the assignments, a midterm examination, and a final examination. Assignments. 1. Each assignment will be due two weeks after it is handed out. 2. Assignments must be submitted electronically using the WebCT assignment tool. 3. Assignments will be marked promptly by the TA; marks and comments on A new module will be made available each week, the associated assignment will be due two weeks later. TEACHING ASSISTANT The teaching assistant for the course will be Daniel Ludvig (e‐mail: daniel.ludvig@mcgill.ca) 1 September 2009 3/5 BMDE: 519 ANALYSIS OF BIOMEDICAL SIGNALS AND SYSTEMS Outline & Information each assignment will be made available electronically on WebCT. 4. Assignments will be graded primarily on their content but must be presented neatly and concisely; marks will be deducted for inadequate presentation. Course notes and assignments. These will be made available prior to each class and it will be your responsibility to download and print these if you so desire. Material will be made available as pdf files for downloading and printing. You will need a copy of the Acrobat reader to view and print pdf files. All matlab m‐files and data sets required for the assignments will be made available electronically by way of WebCT. Electronic submission of assignments and feedback of marks and comments from the instructor. Private e‐mail system for course‐ related correspondence between members of the class, the instructor and TA Private discussion forum It is essential that students keep up to date with assignments; late assignments will be subject to a 10%/day penalty. 5. The mid‐term examination will consist of a “take‐home” project requiring the independent analysis of a test data set; it will cover the material from the first five modules. The final examination will consist of a “take‐ home” project requiring the independent analysis of a test data set; it will cover material from all ten modules. Provide hints and an FAQ list The final grade will be determined using the following algorithm: Links to relevant reference material TG .5 * AS .15 * max( ME , FE ) .35 * FE Calendar of course events where Students may login to course through the url: TG final grade % AS assignment grade % http://www.mcgill.ca/mycourses/ ME mid-term exam grade % M ATLAB FE final exam grade % WEBCT All demonstrations and analysis procedures will be done using MATLAB ‐ a high‐performance numeric computation and visualization software package. Although this is not a course in computer science or programming, it will be necessary to become familiar with MATLAB and do some simple programming in it. WebCTVista a web based instructional computing system will be used as a resource in the course to provide: Exercises and assignments require MATLAB and the signal processing toolbox. If you do not have access to MATLAB at present you may: Students with a failing grade may undertake to improve their standing by performing additional assignments at the discretion of the instructor and provided that all assignments have been submitted. 1 September 2009 4/5 BMDE: 519 ANALYSIS OF BIOMEDICAL SIGNALS AND SYSTEMS Outline & Information use Matlab installed on computers in student laboratories or the research computers in your supervisor’s laboratory. purchase the student version of MATLAB and install it on your own computer. The student version is available through the McGill Computing Store. The preferred version of MATLAB (R2009a); this version is used to develop and test the assignments. Earlier versions of MATLAB may encounter unexpected problems. An introduction to Matlab is available from the Mathworks web site at: http://www.mathworks.com/access/helpdesk/help/ techdoc/matlab.shtml McGill University values academic integrity. Therefore all students must understand the meaning and consequences of cheating, plagiarism and other academic offences under the Code of Student Conduct and Disciplinary Procedures. See http://www.mcgill.ca/integrity/ for more information. EXTRAORDINARY CIRCUMSTANCES “In the event of extraordinary circumstances beyond the University’s control, the content and/or evaluation scheme in this course is subject to change.” L ANGUGE OF SUBMISSION Printable versions of these manuals are also available at this site. Two manuals of particular interest are: ACADEMIC INTEGRITY In accord with McGill University’s Charter of Students’ Rights, students in this course have the right to submit in English or in French any written work that is to be graded. Getting Started with MATLAB Using MATLAB Additional introductory information about Matlab is available at: http://blogs.mathworks.com/pick/category/video/ SEE THE WEB LINKS TOOL IN WEBCT PAGE FOR THE COURSE. 1 September 2009 5/5 ...
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