Uniform FIR approximation of causal Wiener filters with applications to causal coherence

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

Department dc:contributor.department

Massachusetts Institute of Technology. Department of Electrical Engineering and Computer Science.

Grantor dc:publisher

Massachusetts Institute of Technology

Year dc:date.issued

2015

Author dc:creator

• Barnes, Leighton P. (Leighton Pate)

Advisor dc:contributor.advisor

• George Verghese.

• Electrical Engineering and Computer Science.

Statement dc:rights

• 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.

Licence dc:rights.uri

• http://dspace.mit.edu/handle/1721.1/7582

Language dc:language.iso

eng

Handle dc:identifier.uri

http://hdl.handle.net/1721.1/100295

OAI identifier oai:identifier

oai:dspace.mit.edu:1721.1/100295