Parameter Estimation of a Noisy Real Sinusoid Using Quartic Polynomial Approach

Abstract

An analytical polynomial expression, for accurate and computationally efficient frequency estimation of a single real sinusoid under Additive White Gaussian Noise (AWGN), is derived and proposed in this paper. The method, which can be easily adapted for real time frequency estimation, is based on transforming the frequency estimation problem as the solution of a fourth order (quartic) expressed as powers of a trigonometric function containing the unknown frequency. The coefficients of the quartic polynomial can be found using the complex magnitudes of three Discrete Fourier Transform (DFT) bins, centered at the maximum magnitude value of the DFT coefficients. Simulated results illustrate that, the performance of the proposed estimator has a mean squared-error (MSE) performance which is very close to the Cramer Rao Lower Bound (CRLB) for high signal-to-noise ratio (SNR) region, as well as close to previously published estimators in the low SNR region.