A simple method for precise estimation of sinusoidal frequency

This paper proposes a method for precisely estimating sinusoidal frequency using five samples. The estimation procedure is implemented by interpolating the impulse location between DFT results. Five samples are used because two complex components are available in the DFT results. However, an estimat...

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Bibliographic Details
Published inElectronics & communications in Japan. Part 3, Fundamental electronic science Vol. 75; no. 4; pp. 92 - 100
Main Authors Noro, Yuichi, Inomoto, Kenji, Kuno, Kazuhiro
Format Journal Article
LanguageEnglish
Published New York Wiley Subscription Services, Inc., A Wiley Company 1992
Subjects
digital signal processing
Discrete Fourier transform
frequency estimation
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Summary:This paper proposes a method for precisely estimating sinusoidal frequency using five samples. The estimation procedure is implemented by interpolating the impulse location between DFT results. Five samples are used because two complex components are available in the DFT results. However, an estimation method which uses four samples and is called Prony's approximation method is known in the literature. To derive interpolation formulas for six or more samples is more complex. In this paper, strict estimation formulas and their simplified versions are deduced from the DFTs of five samples. The frequency estimation error is also discussed with a computer‐simulated experiment which shows a 1 percent r.m.s. error at a signal‐to‐noise ratio of 30 dB. This method may be applicable for representing frequency in a direct binary form which can be processed by simple operations such as addition, exclusive‐OR, and sign extractions form the calculated value.
Bibliography:istex:32D6C0BBAB52C3A5C1904044CE55F71697499B68
ark:/67375/WNG-3W85F0R6-P
ArticleID:ECJC4430750409
Kenji Inomoto received a B.S. and an M.S. in Electrical Engineering from Gifu University in 1969 and 1971 and received a Dr. Eng. from Nagoya University in 1979. In 1971 he joined Mie University as an Assistant Professor and was an Associate Professor in 1983. Presently, he is a Professor of Medical Science and Technology at Suzuka University. He is a member of IEEE and his research interests are in signal processing.
Kazuhiro Kuno received a B.S. and a Dr. Eng. in Electrical Engineering from Nagoya University, Nagoya, Japan, in 1964 and 1971, respectively. In 1969 he was an Assistant Professor and in 1978 an Associate Professor of Electrical Engineering at Nagoya University. In April 1987, he joined the Faculty of the Department of Electrical and Electronics Engineering Department, Mie University, where he is a Professor. His current interests are in theoretical acoustics, reverberation theory, noise and vibration, and statistical data analysis, etc.
Yuichi Noro received a B.S. and an M.S. in Electrical Engineering from Mie University, Mie Prefecture, Japan, in 1984 and 1986, respectively. Since 1986, he has been an Assistant Professor of the Department of Electrical and Electronics Engineering, Mie University. His current research interests are sound field theory, environmental noise analysis, and digital signal processing.
ISSN:1042-0967
1520-6440
DOI:10.1002/ecjc.4430750409