ECE 735 Signal Synthesis and Recovery Techniques, Lec. 1, Fall 1998

Instructor:     John A. Gubner, Associate Professor, ECE Department.
                Office: 3615 Engr. Hall.
                Phone: 263-1471.
                E-mail: gubner@engr.wisc.edu

Credits:        3

Prerequisites:  ECE 431 or ECE 533 or consent of instructor.

Goals & Topics:

      The main goal of this course is to introduce some basic
  tools that are useful in analyzing signal synthesis/recovery problems.
  In such problems, a signal or image (call it x) passes through a system
  and produces an output y.  Based on a knowledge of the system and its
  output, one would like to find the corresponding system input.
  Depending on the context, this can be viewed as a signal synthesis
  problem, or a signal recovery problem.  If the output y represents
  measured data, then finding the input x is regarded as a recovery
  problem, e.g., image deblurring.  On the other hand, if y is a
  specified design constraint, finding x is regarded as a signal
  synthesis problem, e.g., signal-set design for digital communication
  channels.

      Some of the tools we will study include: projections, pseudo-inverses,
  diagonalization, the singular-value decomposition, and regularization,
  all for infinite-dimensional systems.  Other topics to be covered
  include collocation using splines, minimum time-bandwidth product,
  short-time Fourier transforms, and continuous-time wavelet transforms.
  To conclude the course, we introduce some nonlinear signal recovery
  algorithms such as contraction mappings and alternating projections
  onto convex sets.

      Homework assignments will vary, with some requiring analysis and
  others requiring algorithm implementation using MATLAB.

Textbooks:      Required: None.

                Optional: Optimization by Vector Space Methods,
                          D. G. Luenberger.

                          A Primer on Integral Equations of the First Kind,
                          G. M. Wing.

Computer Usage: Some homework assignments require MATLAB.

Papers:         None.

Project:        None.

Grading Policy: Homework 20%
                Exam 1   40%
                Exam 2   40%