2026-09-19T13:10:31Zhttps://dspace.mit.edu/server/oai/requestoai:dspace.mit.edu:1721.1/1002952026-06-06T00:48:38Zcom_1721.1_7582com_1721.1_7581col_1721.1_131023
George Verghese.
Barnes, Leighton P. (Leighton Pate)
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.
Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science
2015-12-16T15:54:03Z
2015-12-16T15:54:03Z
2015
2015
http://hdl.handle.net/1721.1/100295
930612887
Thesis: M. Eng., Massachusetts Institute of Technology, Department of Electrical Engineering and Computer Science, 2015.
This electronic version was submitted by the student author. The certified thesis is available in the Institute Archives and Special Collections.
Cataloged from student-submitted PDF version of thesis.
Includes bibliographical references (pages 35-36).
Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation
by Leighton P. Barnes.
M.Eng.
36 pages
eng
Massachusetts Institute of Technology
M.I.T. theses are protected by copyright. They may be viewed from this source for any purpose, but reproduction or distribution in any format is prohibited without written permission. See provided URL for inquiries about permission.
http://dspace.mit.edu/handle/1721.1/7582
Electrical Engineering and Computer Science.
Uniform FIR approximation of causal Wiener filters with applications to causal coherence
Thesis
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<Abstract>Leveraging the relationship between Wiener filtering and the coherence function, a version of coherence is defined that captures the causal relationship between WSS processes. This causal coherence is interpreted in a modeling context and used to demonstrate what a frequency dependent measure for causality both can and can't represent. To understand how well frequency dependent coherence spectra can be estimated with finite order approximations, the convergence of the FIR causal Wiener lters to the full IIR causal Wiener filter is investigated as filter length goes to infinity. The main results prove Lp convergence of the frequency responses for p = 1, 2, [infinity] under certain Hölder continuity conditions on the power spectra, as well as give asymptotic upper bounds for the convergence error. Keywords: Wiener lters, causality, coherence, FIR approximation</Abstract>
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