Sinusoidal Frequency EstimationThe form of the least-squares estimator (5.41) in the known-frequency case immediately suggests the following frequency estimator for the unknown-frequency case:
That is, the sinusoidal frequency estimate is defined as that frequency which maximizes the DTFT magnitude. Given this frequency, the least-squares sinusoidal amplitude and phase estimates are given by (5.41) evaluated at that frequency. It can be shown  that (5.43) is in fact the optimal least-squares estimator for a single sinusoid in white noise. It is also the maximum likelihood estimator for a single sinusoid in Gaussian white noise, as discussed in the next section. In summary,
In practice, of course, the DTFT is implemented as an interpolated FFT, as described in the previous sections (e.g., QIFFT method).
Multiple Sinusoids in Additive Gaussian White Noise
Sinusoidal Amplitude and Phase Estimation