Exact and approximate polynomial decomposition methods for signal processing applications
Author(s)Demirtas, Sefa; Su, Guolong; Oppenheim, Alan V.
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Signal processing is a discipline in which functional composition and decomposition can potentially be utilized in a variety of creative ways. From an analysis point of view, further insight can be gained into existing signal processing systems and techniques by reinterpreting them in terms of functional composition. From a synthesis point of view, functional composition offers new algorithms and techniques with modular structure. Moreover, computations can be performed more efficiently and data can be represented more compactly in information systems represented in the context of a compositional structure. Polynomials are ubiquitous in signal processing in the form of z-transforms. In this paper, we summarize the fundamentals of functional composition and decomposition for polynomials from the perspective of exploiting them in signal processing. We compare exact polynomial decomposition algorithms for sequences that are exactly decomposable when expressed as a polynomial, and approximate decomposition algorithms for those that are not exactly decomposable. Furthermore, we identify efficiencies in using exact decomposition techniques in the context of signal processing and introduce a new approximate polynomial decomposition technique based on the use of Structured Total Least Norm (STLN) formulation.
DepartmentMassachusetts Institute of Technology. Department of Electrical Engineering and Computer Science; Massachusetts Institute of Technology. Research Laboratory of Electronics
Proceedings of the 2013 IEEE International Conference on Acoustics, Speech and Signal Processing
Institute of Electrical and Electronics Engineers (IEEE)
Demirtas, Sefa, Guolong Su, and Alan V. Oppenheim. “Exact and Approximate Polynomial Decomposition Methods for Signal Processing Applications.” 2013 IEEE International Conference on Acoustics, Speech and Signal Processing (May 2013).
Author's final manuscript