Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)
Summary :
Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E83-A No.9 pp.1739-1747
- Publication Date
- 2000/09/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- PAPER
- Category
- Digital Signal Processing
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Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, "Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)" in IEICE TRANSACTIONS on Fundamentals,
vol. E83-A, no. 9, pp. 1739-1747, September 2000, doi: .
Abstract: Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e83-a_9_1739/_p
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@ARTICLE{e83-a_9_1739,
author={Yegui XIAO, Takahiro MATSUO, Katsunori SHIDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)},
year={2000},
volume={E83-A},
number={9},
pages={1739-1747},
abstract={Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.},
keywords={},
doi={},
ISSN={},
month={September},}
Copy
TY - JOUR
TI - Performance Analyses of Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform (CNFT)
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1739
EP - 1747
AU - Yegui XIAO
AU - Takahiro MATSUO
AU - Katsunori SHIDA
PY - 2000
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E83-A
IS - 9
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - September 2000
AB - Fourier analysis of sinusoidal and/or quasi-periodic signals in additive noise has been used in various fields. So far, many analysis algorithms including the well-known DFT have been developed. In particular, many adaptive algorithms have been proposed to handle non-stationary signals whose discrete Fourier coefficients (DFCs) are time-varying. Notch Fourier Transform (NFT) and Constrained Notch Fourier Transform(CNFT) proposed by Tadokoro et al. and Kilani et al., respectively, are two of them, which are implemented by filter banks and estimate the DFCs via simple sliding algorithms of their own. This paper presents, for the first time, statistical performance analyses of the NFT and the CNFT. Estimation biases and mean square errors (MSEs) of their sliding algorithms will be derived in closed form. As a result, it is revealed that both algorithms are unbiased, and their estimation MSEs are related to the signal frequencies, the additive noise variance and orders of comb filters used in their filter banks. Extensive simulations are performed to confirm the analytical findings.
ER -
English
