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A Simple and Explicit Formulation of NonUnique Wiener Filters for Linear Predictor with RankDeficient Autocorrelation Matrix
Shunsuke KOSHITA Masahide ABE Masayuki KAWAMATA Takaaki OHNARI Tomoyuki KAWASAKI Shogo MIURA
Publication
IEICE TRANSACTIONS on Fundamentals of Electronics, Communications and Computer Sciences
Vol.E99A
No.8
pp.16141617 Publication Date: 2016/08/01 Online ISSN: 17451337
DOI: 10.1587/transfun.E99.A.1614 Type of Manuscript: LETTER Category: Digital Signal Processing Keyword: Wiener filter, linear predictor, noisefree input, rankdeficient input autocorrelation matrix,
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Summary:
This letter presents a simple and explicit formulation of nonunique Wiener filters associated with the linear predictor for processing of sinusoids. It was shown in the literature that, if the input signal consists of only sinusoids and does not include a white noise, the input autocorrelation matrix in the WienerHopf equation becomes rankdeficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rankdeficient problem and present a mathematical description of nonunique Wiener filters in a simple and explicit form. This description is directly obtained from the tap number, the frequency of sinusoid, and the delay parameter. We derive this result by means of the elementary row operations on the augmented matrix given by the WienerHopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.

