A Highly Accurate Algorithm for the Estimation of the Frequency of a Complex Exponential in Additive Gaussian Noise

A new algorithm for the precise estimation of the frequency of a complex exponential signal ill additive, complex, white Gaussian noise Is presented. The algorithm has low computational complexity and is well suited for numerous real time applications. The DIT based algorithm performs an initial coarse frequency estimation using the peak search of an N point complex Fast Fourier Transform. The algorithm forms a frequency estimate using a functional mapping from two modified DIT coefficients which are one half DIT frequency bin below and above largest magnitude FFT coefficient. Recursion is used to provide frequencies of the modified DFT coefficients which minimize the variance of the frequency estimation error. For large N and large signal to noise ratio, the frequency estimation error variance obtained is 0.063 dB above the Cramer-Rae Bound. This excellent performance is achieved with low computational complexity. The algorithm provides exact frequency determination in the noiseless case.