The form of the least-squares estimator (5.41) in the known-frequency case immediately suggests the following frequency estimator for the unknown-frequency case:
It can be shown [121] 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).