A Combined Method for Estimating the Frequency of a Complex Exponential

A method based on the theory of Random Basic Functions (RBF) has recently been proposed for estimating the frequency of a noisy complex exponential. This method has less computational complexity compared to the common method that uses periodogram. The most significant drawback of this RBF method is its poor performance and relatively large errors in low signal to noise ratios. In this paper, we propose a combined frequency estimation method based on both periodogram and RBF methods which has much better performance compared to the RBF and periodogram methods. The computational complexity of the proposed method is less than or equal to that of RBF method. In the proposed combined method, a short length periodogram is evaluated for available data at first. Then, an initial estimate for the exponential frequency is obtained based on the evaluated periodogram. The final estimate for the exponential frequency is obtained using the RBF method and the initial estimate obtained from periodogram. In this paper, we also show that the proposed combined method performs well for nonuniform sampling cases. The performance of RBF method, periodogram method, and proposed combined method are compared using numerical simulations.