Estimating the frequency of a noisy sinusoid by linear regression
IEEE Transactions on Information Theory
List of references on spectral line analysis
Signal Processing
Approximate maximum likelihood frequency estimation
Automatica (Journal of IFAC) - Special issue on statistical signal processing and control
A method of extraction of nonstationary sinusoids
Signal Processing
A new IIR adaptive notch filter
Signal Processing
Frequency estimation from proper sets of correlations
IEEE Transactions on Signal Processing
On the performance of the weighted linear predictor frequencyestimator
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Iterative frequency estimation by interpolation on Fourier coefficients
IEEE Transactions on Signal Processing
Estimation of frequency, amplitude, and phase from the DFT of atime series
IEEE Transactions on Signal Processing
Fast algorithms for single frequency estimation
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
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In this paper, we propose a novel method for estimating the parameters (frequency, amplitude, and phase) of real sinusoids. To derive the estimator, we start from the characteristic differential equation of a sinusoid. To remove differentials and obtain an algebraic relation for frequency, we introduce finite-period weighted integrals of the differential equation, which become equivalent to the differential equation when a sufficient number of weight functions are applied. As weight functions, we show that Fourier kemels have excellent properties. Terms related to integral boundaries are readily eliminated, observations are provided by Fourier coefficients, and the relation becomes independently accurate for multiple sinusoids if they are sufficiently spaced. We solve the obtained equations in two ways: one is for approaching to the Cramér-Rao lower bound (CRLB), and the other is for enhancing the interference rejection capability. Also, methods are proposed to calculate the weighted integrals from sampled signals with an improved accuracy. Proposed algorithms are examined under noise and sinusoidal interference. Error variances are compared with the CRLB and other fast Fourier transform (FFT)-based methods.