Estimation of frequencies of sinusoids in the presence of noise

A method is proposed and developed for estimating the frequencies of K sinusoids given the sum of these sinusoids in Gaussian noise. Attention is focused on the properties of these estimators when the observation time is short, the separation between frequencies is small, and the signal‐to‐noise ratio is high. The estimators are shown to be approximately unbiased and approximately normally distributed. The covariance matrix is also calculated. Relatively simple bounds on the variance of the estimators are found.