A Simple and Explicit Formulation of Non-Unique Wiener Filters for Linear Predictor with Rank-Deficient Autocorrelation Matrix

Shunsuke KOSHITA; Masahide ABE; Masayuki KAWAMATA; Takaaki OHNARI; Tomoyuki KAWASAKI; Shogo MIURA

doi:10.1587/transfun.E99.A.1614

A Simple and Explicit Formulation of Non-Unique Wiener Filters for Linear Predictor with Rank-Deficient Autocorrelation Matrix

Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, Takaaki OHNARI, Tomoyuki KAWASAKI, Shogo MIURA

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This letter presents a simple and explicit formulation of non-unique 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 Wiener-Hopf equation becomes rank-deficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rank-deficient problem and present a mathematical description of non-unique 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 Wiener-Hopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E99-A No.8 pp.1614-1617

Publication Date: 2016/08/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E99.A.1614

Type of Manuscript: LETTER

Category: Digital Signal Processing

Authors

Shunsuke KOSHITA
  Tohoku University
Masahide ABE
  Tohoku University
Masayuki KAWAMATA
  Tohoku University
Takaaki OHNARI
  TOSHIBA Corporation
Tomoyuki KAWASAKI
  TOSHIBA Corporation
Shogo MIURA
  TOSHIBA Corporation

Keyword

Wiener filter, linear predictor, noise-free input, rank-deficient input autocorrelation matrix

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Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, Takaaki OHNARI, Tomoyuki KAWASAKI, Shogo MIURA, "A Simple and Explicit Formulation of Non-Unique Wiener Filters for Linear Predictor with Rank-Deficient Autocorrelation Matrix" in IEICE TRANSACTIONS on Fundamentals, vol. E99-A, no. 8, pp. 1614-1617, August 2016, doi: 10.1587/transfun.E99.A.1614.
Abstract: This letter presents a simple and explicit formulation of non-unique 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 Wiener-Hopf equation becomes rank-deficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rank-deficient problem and present a mathematical description of non-unique 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 Wiener-Hopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E99.A.1614/_p

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@ARTICLE{e99-a_8_1614,
author={Shunsuke KOSHITA, Masahide ABE, Masayuki KAWAMATA, Takaaki OHNARI, Tomoyuki KAWASAKI, Shogo MIURA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={A Simple and Explicit Formulation of Non-Unique Wiener Filters for Linear Predictor with Rank-Deficient Autocorrelation Matrix},
year={2016},
volume={E99-A},
number={8},
pages={1614-1617},
abstract={This letter presents a simple and explicit formulation of non-unique 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 Wiener-Hopf equation becomes rank-deficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rank-deficient problem and present a mathematical description of non-unique 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 Wiener-Hopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.},
keywords={},
doi={10.1587/transfun.E99.A.1614},
ISSN={1745-1337},
month={August},}

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TY - JOUR
TI - A Simple and Explicit Formulation of Non-Unique Wiener Filters for Linear Predictor with Rank-Deficient Autocorrelation Matrix
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1614
EP - 1617
AU - Shunsuke KOSHITA
AU - Masahide ABE
AU - Masayuki KAWAMATA
AU - Takaaki OHNARI
AU - Tomoyuki KAWASAKI
AU - Shogo MIURA
PY - 2016
DO - 10.1587/transfun.E99.A.1614
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E99-A
IS - 8
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - August 2016
AB - This letter presents a simple and explicit formulation of non-unique 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 Wiener-Hopf equation becomes rank-deficient and thus the Wiener filter is not uniquely determined. In this letter we deal with this rank-deficient problem and present a mathematical description of non-unique 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 Wiener-Hopf equation. We also show that the conventional Wiener filter for noisy input signal is included as a special case of our description.
ER -