Digital Signal Processing

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					                                Delaware State University
                        Applied Mathematics and Theoretical Physics Department
                                             Dover, DE 19901

Digital Signal Processing
60-787-00,          3 credits

Text books:
J. G. Proakis, D. K. Manolakis:
Digital Signal Processing, Prentice-Hall, 2007
Recommended text books:
J. McClellan, C. Burrus, A. Oppenheim, T. Parks, Schafer/ Schuessler:
Computer Base Exercises for Signals Processing using Matlab Version 5
Oppenheim & Willsky:
Signals and Systems

        The goal of this course is to provide the student with the mathematical tools and techniques for
analyzing, modeling, and implementing digital signal processing systems. This course also provides the
relevant background knowledge to students of applied mathematics and theoretical physics who need the
signal processing tools for the analysis of data obtained during research in their fields.


Prerequisite: Complex Analysis (60-571) and Differential Equations (60-5xx) (Recommended)
        Successful students are expected to gain a practical knowledge of the covered material and to be
able to: 1) follow the applications in the literature, 2) solve typical problems in the field, 3) apply the
theoretical knowledge on real data using methods presented in class lectures and 4) improve their
programming skills through the use of software packages such as MATLAB.


Topical schedule:
  1.   Introduction
  2.   Discrete-Time Signals and Systems
  3.   The Z-Transform and its Application to the Analysis of Linear Time Invariant (LTI) Systems
  4.   Frequency Analysis of Signals and Systems
  5.   Frequency Domain Analysis of LTI Systems
  6.   Sampling and Reconstruction of Signals
  7.   The Discrete Fourier Transform (DFT): its Properties and Applications
  8.   Efficient Computation of the DFT: Fast Fourier Transform Algorithms
  9.   Implementation of Discrete-Time Systems
 10.   Design of Digital Filers
 11.   Multirate Digital Signal Processing
 12.   Linear Prediction and Optimum Linear Filters
 13.   Adaptive Filters
 14.   Power Spectrum Estimation
CURRICULUM COURSE REVIEW                                                               Digital Signal Processing




  1. Course Title/Number:               Digital Signal Processing / 60-787-00

  2. Number of Credits:                 3

  3. Curriculum Program Title:          Ph.D. in Applied Mathematics and Theoretical Physics

  4. Curriculum/Course is:              [X]      New                          [   ]   Revised
                                        [   ]    Required Course              [X]     Elective Course

  5. List Prerequisites:
        Complex Analysis (60-571)
        Ordinary Differential Equations (60-551) (Recommended)

  6. List Courses Being Replaced or Changed:
        This is a new course.

  7. List Courses Being Deleted:
        No courses are being deleted.

  8. Needs Statement:
        This course is needed for students pursuing a Ph.D. in several areas of applied mathematics and
theoretical physics. The digital approach has replaced analog techniques in many applications due to its
numerous advantages: it enables robustness and predictable high quality of processed and stored signals
and data. The course provides the fundamental training in this area and the essential programming skills
to applied mathematicians interested in doing research in audio and visual signal processing. This course
also provides the useful tools to theoretical physicists who need to process various kinds of data needed
in their research.

  9. Catalog Description of the Course:
        This course provides the student with the mathematical tools and techniques for analyzing,
modeling, and implementing digital signal processing systems. This course also provides the relevant
background knowledge to students of applied mathematics and theoretical physics who need the signal
processing tools for the analysis of data obtained during research in their fields.
CURRICULUM COURSE REVIEW                                                                Digital Signal Processing

 10. List of Objectives of the Course:
       (1) To provide students with fundamental knowledge and techniques in signal processing. (2) To
apply these techniques to the analysis of real world data in various fields of science. (3) To learn how to
apply the described methods in MATLAB and how to develop the algorithms based on mathematical
modeling. (4) To develop the problem-solving skills associated with the application of these methods in
practical, real data processing, and learn how to extract verifiable information from such applications.

 11. Course Outline:
       See the “Topical schedule” section in the attached brief syllabus.

 12. Show how the proposed course fits into the curriculum or course sequence:
       This course is an elective within the curriculum of the Ph.D. program in applied mathematics and
theoretical physics. It is important for students of both applied mathematics and theoretical physics
whose research will require processing large amounts and various types of real world data and extracting
useful information from it. The prerequisites are listed in item 5.

 13. Are there comparable courses in other departments?
       No.

 14. How will the students be affected by this course change?

       This course provides the students an opportunity to increase their integration with the research
program of the Department of Applied Mathematics and Theoretical Physics, by enabling them with
knowledge and programming skills necessary for most of their research fields. This course will improve
students’ professional competence, employability in technical fields and ability to pass professional
examinations. Neither this course nor its prerequisites increase the total number of semester hours in this
curriculum or the number of credit hours required for graduation.


 15. What effect will this new course have on College resource?
       None. This course will not require new or additional resources or staffing.

 16. How will the course benefit the College?
       It is very probable that some of Applied Mathematics and Theoretical Physics students during
their studies and later in their profession will deal with lot of data as a part of their research or common
work. That is why it is essential for them to be familiar with signal and data processing tools and
algorithms that will increase the quality of their study and research. The proposed course may become a
CURRICULUM COURSE REVIEW                                                              Digital Signal Processing

critical supplement to the existing curriculum of the Applied Mathematics and Theoretical Physics
program at Delaware State University. The fact that the similar courses have already been established in
graduate curriculum in many universities in the US confirms the usefulness of this course. The Digital
Signal Processing course will qualify students to work in their fields and to pursue an advanced degree
in this domain. It may provide the students with strong background in data processing and thus secure a
wider job market. It will also provide them the knowledge of using the computer and specialized
software for data analysis, which will make them competitive in the field and it will widen their
knowledge.

 17. How will the change affect the program?
       This course will introduce students to a few select topics in “higher” mathematics and their
application in various branches of various data analysis in the fields of applied mathematics and physics.
This course will be one of the electives specific to the Ph.D. program in this department. Besides
providing such a cross-disciplinary broadening of knowledge for the students in this program, it will
provide practical knowledge and training in programming.

 18. Evaluation of Student Performance:
       Homework Assignments                  30 %
       Two (2) in-term examinations          30 %
       Final Examination                     40 %
       Sample homework assignments, in-term and final examination question-sheets, course notes and
review sheets will be accessible on-line.

       Course Structure: Two (2) 75-minute lectures per week.

References
   1. J. G. Proakis, D. K. Manolakis: “Digital Signal Processing”, Prentice-Hall, 2007.
   2. J. McClellan, C. Burrus, A. Oppenheim, T. Parks, Schafer/ Schuessler: “Computer Base Exercises
   for Signals Processing using Matlab Version 5”, Prentice-Hall, 1998.
   3. Oppenheim & Willsky: “Signals and Systems”, 2nd Edition, Prentice-Hall, 1997.

Submitted to Department of Applied Mathematics and Theoretical Physics
by: Vesna Zeljkovic, on 27th of November, 2007

				
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