EEE 550 – Transform Theory and Applications
Fall 2010Course Information
InstructorDouglas CochranTelephone:(480) 965-7409
Office:GWC 664E-mail:
Office hours:Tuesdays and Thursdays, 11:00 – 12:00 pm (or by appointment)
DescriptionEEE 550 is a one-semester graduate course that elaborates on the mathematical foundations of linear signal and system analysis. General concepts underpinning linear synthesis and analysis of signals in normed linear spaces and inner product spaces will be introduced, including bases, frames, projection and approximation, and convergence in infinite-dimensional spaces. General foundations of linear operator theory will also be developed. These general concepts will be exemplified in familiar settings such as Fourier and wavelet analysis. Coherent states and group actions on signal spaces will be introduced. Elements of Lebesgue measure and integration as well as complex function theory will be introduced as needed to support the central themes of the course.
BackgroundThis class is intended for graduate students in electrical engineering and applied mathematics whose research work demands understanding of harmonic analysis beyond what is covered in first-year graduate courses in signal processing, communication theory, or control theory. Students should already have taken several classes in one or more of these areas in order to make connections of the mathematical concepts in this course to applications.Most of the course material consists of theorems, proofs, and examples; there are no computer assignments or projects intended to emphasize applications. Although there is no formal pre-requisite, this is an advanced class.
ClassTuesdays and Thursdays, 7:30 – 8:45 am in room [TBA].
Meetings
TextNone. Several sources of reference material will be made available for download or on library reserve.
HomeworkThree problem sets will be assigned during the semester. The problems will be difficult and two to three weeks will be allotted for completion of each assignment. Collectively, they will count for 60% of the course grade. Since solutions will be distributed on the due dates,late homework will not be accepted unless prior arrangements have been established.
HomeworkStudents are encouraged to discuss homework problems and projects at a general level,
Collaborationbut each person must prepare assignment submissions individually. If two assignments are sufficiently similar in detail to indicate collaboration at more than a conceptual level, both will receive scores of zero.
ExamsAn in-class midterm exam will be held on Thursday, October 21st. It will not count toward the course grade, rather is offered as a self-assessment vehicle. The final exam is scheduled for Tuesday, December 14th from 7:30 am until 9:20 am. The final counts for 40% of the course grade.
RequiredA computer account supporting internet www access via browser. Assignments,
Toolssolutions, and other materials given out is class will also be available via the myASU electronic blackboard service.
UsefulD. Cochran, Notes on Transform Theory and Applications*
ReferenceI. Daubechies, Ten Lectures on Wavelets
MaterialsH. Dym and H.P. McKean,Fourier Series and Integrals
C. Heil, A Basis Theory Primer*
C. Heil, Banach and Hilbert Space Review*
C. Heil, Real Analysis Review*
A. Papoulis, Signal Analysis
W. Rudin, Real and Complex Analysis
A. Terras, Fourier Analysis on Finite Groups
*Available for download from the course webpage.
TopicsLinear Signal Spaces
Linear space
Norms, Banach space
Inner products, Hilbert space
Signal representation (analysis and synthesis)
Orthonormal bases
Riesz bases
Frames
Approximation
Linear transforms
Linear operators
Operator norm, boundedness and continuity
Riesz representation theorem
Integral transforms
Fourier transforms
Fourier-Lebesgue theorem
Complex extensions, Laplace and Z transforms
Wavelet transforms
Coherent states
Group actions
Weyl-Heisenberg and affine theory
Balian-Low Theorem
Sampling Theory
Whittaker-Kotel’nikov-Shannon theorem
Reproducing kernel Hilbert space
A1. Measure and Lebesgue integration
A2. Complex integration
AcademicAbsolute professionalism in matters of academic integrity is expected. The minimum
Integritypenalty for collaboration on the final examination in this class will be a grade of E for the class; expulsion from ASU may be sought. Other forms of academic misconduct will also incur harsh penalties.
GradeOccasionally mistakes are made in marking papers and in assigning course grades. In the
Appealsformer case, students should write a brief explanation of the putative grading mistake and submit it along with the original work for re-evaluation. In the latter case, a written appeal that explains the suspected grading error should also be submitted. Verbal appeals will not be entertained in either case.