Doctoral Thesis: Functional Composition and Decomposition for Signal Processing

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Event Speaker: 

Sefa Demirtas

Event Location: 

36-428 (Haus Room)

Event Date/Time: 

Thursday, May 8, 2014 - 10:00am

 

Abstract:

Functional composition, the application of one function to the results
of another function, has a long history in the mathematics community,
particularly in the context of polynomials and rational functions. This
thesis articulates and explores a general framework for the use of
functional composition in the context of signal processing. Its many
potential applications to signal processing include utilization of the
composition of simpler or lower order subfunctions to exactly or
approximately represent a given function or data sequence. Although
functional composition currently appears implicitly in a number of
established signal processing algorithms, it is shown how the more
general context developed and exploited in this thesis leads to
significantly improved results for several important classes of
functions that are ubiquitous in signal processing such as polynomials,
frequency responses and discrete multivariate functions. Specifically,
the functional composition framework is exploited in analyzing,
designing and extending modular filters, separating marginalization
computations into more manageable subcomputations and representing
discrete sequences with fewer degrees of freedom than their length and
region of support with implications for sparsity and efficiency.

Advisor: Prof. Alan V. Oppenheim
Committee: Prof. Pablo A. Parrilo and Prof. George C. Verghese