Minimum Length of a Signal for Fundamental Frequency Estimation and Its Application

Takahiro MURAKAMI; Hiroyuki YAMAGISHI; Yoshihisa ISHIDA

doi:10.1587/transfun.E98.A.1914

Minimum Length of a Signal for Fundamental Frequency Estimation and Its Application

Takahiro MURAKAMI, Hiroyuki YAMAGISHI, Yoshihisa ISHIDA

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The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.

Publication: IEICE TRANSACTIONS on Fundamentals Vol.E98-A No.9 pp.1914-1923

Publication Date: 2015/09/01

Publicized

Online ISSN: 1745-1337

DOI: 10.1587/transfun.E98.A.1914

Type of Manuscript: PAPER

Category: Digital Signal Processing

Authors

Takahiro MURAKAMI
  Meiji University
Hiroyuki YAMAGISHI
  Tokyo Metropolitan College of Industrial Technology
Yoshihisa ISHIDA
  Meiji University

Keyword

CRLB, fundamental frequency estimation, length of a signal, pitch estimation

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Takahiro MURAKAMI, Hiroyuki YAMAGISHI, Yoshihisa ISHIDA, "Minimum Length of a Signal for Fundamental Frequency Estimation and Its Application" in IEICE TRANSACTIONS on Fundamentals, vol. E98-A, no. 9, pp. 1914-1923, September 2015, doi: 10.1587/transfun.E98.A.1914.
Abstract: The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.
URL: https://globals.ieice.org/en_transactions/fundamentals/10.1587/transfun.E98.A.1914/_p

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@ARTICLE{e98-a_9_1914,
author={Takahiro MURAKAMI, Hiroyuki YAMAGISHI, Yoshihisa ISHIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Minimum Length of a Signal for Fundamental Frequency Estimation and Its Application},
year={2015},
volume={E98-A},
number={9},
pages={1914-1923},
abstract={The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.},
keywords={},
doi={10.1587/transfun.E98.A.1914},
ISSN={1745-1337},
month={September},}

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TY - JOUR
TI - Minimum Length of a Signal for Fundamental Frequency Estimation and Its Application
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1914
EP - 1923
AU - Takahiro MURAKAMI
AU - Hiroyuki YAMAGISHI
AU - Yoshihisa ISHIDA
PY - 2015
DO - 10.1587/transfun.E98.A.1914
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E98-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2015
AB - The theoretically minimum length of a signal for fundamental frequency estimation in a noisy environment is discussed. Assuming that the noise is additive white Gaussian, it is known that a Cramér-Rao lower bound (CRLB) is given by the length and other parameters of the signal. In this paper, we define the minimum length as the length whose CRLB is less than or equal to the specific variance for any parameters of the signal. The specific variance is allowable variance of the estimate within an application of fundamental frequency estimation. By reformulating the CRLB with respect to the initial phase of the signal, the algorithms for determining the minimum length are proposed. In addition, we develop the methods of deciding the specific variance for general fundamental frequency estimation and pitch estimation. Simulation results in terms of both the fundamental frequency estimation and the pitch estimation show the validity of our approach.
ER -