Physics 628 : Digital Time Series Analysis

SPRING 2006

Lectures: MWF 9:15-10:15 AM Room 136 NSCI

Some individual lectures may have to be rescheduled, due to instructor research travel requirements, to a time and place convenient to all.

Texts: Brockwell and Davis, Introduction to Time Series and Forecasting (2nd ed),

Springer, 2002.

Hayes, M.H., Digital Signal Processing, Schaum’s Outline Series, McGraw-Hill, 1999.

Prerequisites : Knowledge of multivariable calculus, elementary statistics, linear algebra, and complex analysis.

Computational Resources : Access to Matlab

Instructor: Davis D. Sentman

Office Hours: MWF, 108 NCSI, 10:30-12:30, directly following class.

Email: dsentman@gi.alaska.edu, NCSI phone 474-5330

Course Content: This course presents general methods used to analyze digitally sampled data that are the normal products of modern research. It is intended primarily for graduate students in physical and social sciences and the engineering disciplines. The course will primarily be lecture oriented, but will include extensive homework sets built around the Matlab package for numerical computations. It will start with a review of linear least squares fitting techniques of sampled data as a way to introduce the concepts of design functions and orthogonality, and then move into uniformly sampled signals. Elementary concepts drawn from statistics, such as random variables, expectation values, and covariance, will be used throughout the course, as will matrix methods from linear algebra. The Fourier Transform and the convolution theorem will be introduced first in the continuous domain, and its discrete form will be presented as a special case of least squares fitting. The relationship between time and frequency domain descriptions of sampled data will be described and methods for computing power spectra developed. Modern methods of Time Series Analysis based on the Z-transform will be covered with emphasis on finite impulse response (moving average) and infinite impulse response (autoregressive) descriptions of processes. Concrete examples from a wide variety of fields will be used to illustrate how these concepts are implemented in computer code.

Homework: Heavy emphasis will be placed on homework. Problems from the texts and custom problems will be assigned routinely. Additional problems may be assigned from other sources appropriate to the topic under discussion. Due dates for the homework will be 1-2 weeks following assignment, depending on the nature of the problem set. .

Examinations: Two examinations in the form of homework sets of greater than usual difficulty will serve as Midterm and Final exams.

Grading: Total points for the course will be weighed as follows:

Homework 50%

Midterm Exam 20%

Final Exam 30%

Student Obligations: Students at UAF are bound by the policies and regulations of the University of Alaska, UAF rules and procedures, and the Student Honor Code, as set forth in the UAF Catalog.