Nonlinear formulas for interpolation, extrapolation, and estimation of single and multiple sinusoids

Author

Ludeman, Lonnie

Author_Institution

Dept. of Electr. & Comput. Eng., New Mexico State Univ., Las Cruces, NM, USA

fYear

1990

fDate

3-6 Apr 1990

Firstpage

2607

Abstract

Formulas for determining frequency, magnitude, and phase of one and two sinusoids are presented. A nonlinear difference equation that all sinusoids must satisfy is also derived for the single sinusoid case. Using the above results, an exact interpolation formula that allows determination of values in a local area of three sampled values for the single sinusoid case and 2N+1 values for N sinusoids is developed. The interpolation formula presented is of a simple symmetric linear form of the sample values, where the coefficients are determined from a nonlinear function involving the distance of the interpolated point from the middle point

Keywords

difference equations; estimation theory; extrapolation; interpolation; spectral analysis; extrapolation; interpolation; local area; middle point; multiple sinusoids; nonlinear difference equation; sampled values; symmetric linear form; Difference equations; Discrete Fourier transforms; Estimation theory; Extrapolation; Frequency; Frequency estimation; Interpolation; Least squares approximation; Phase estimation; Spectral analysis; State estimation;

fLanguage

English

Publisher

ieee

Conference_Titel

Acoustics, Speech, and Signal Processing, 1990. ICASSP-90., 1990 International Conference on

Conference_Location

Albuquerque, NM

ISSN

1520-6149

Type

conf

DOI

10.1109/ICASSP.1990.116146

Filename

116146