Title :
Nonlinear formulas for interpolation, extrapolation, and estimation of single and multiple sinusoids
Author_Institution :
Dept. of Electr. & Comput. Eng., New Mexico State Univ., Las Cruces, NM, USA
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;
Conference_Titel :
Acoustics, Speech, and Signal Processing, 1990. ICASSP-90., 1990 International Conference on
Conference_Location :
Albuquerque, NM
DOI :
10.1109/ICASSP.1990.116146
