  This paper presents an efficient method to compute the maximum likelihood
(ML) estimation of the parameters of a complex 2-D sinusoidal, with the
complexity order of the FFT. The method is based on an accurate barycentric
formula for interpolating band-limited signals, and on the fact that the ML
cost function can be viewed as a signal of this type, if the time and frequency
variables are switched. The method consists in first computing the DFT of the
data samples, and then locating the maximum of the cost function by means of
Newton's algorithm. The fact is that the complexity of the latter step is small
and independent of the data size, since it makes use of the barycentric formula
for obtaining the values of the cost function and its derivatives. Thus, the
total complexity order is that of the FFT. The method is validated in a
numerical example.
