An efficient ML frequency estimation of a sinusoid using the Secant method

The maximum likelihood frequency of a sinusoid is estimated by determining the peak in the frequency domain, and the peak position of any function can be obtained as a root of its derivative. In this paper, we build on this idea and use powerful root-finding algorithms, the Newton-Raphson method and its variant, the Secant method, to estimate the frequency of a signal received in a white Gaussian noise environment. We consider complex exponentials as well as real sinusoids in this work. Our results demonstrate a superior performance in terms of accuracy and efficiency as compared to the existing methods. Furthermore, the proposed method is not sensitive to variations of the frequency and initial phase of the sinusoid.