Examines the statistical properties of the spectral estimators obtained in the analysis of optical signals following photodetection by using a surface acoustic wave (SAW) spectrum analyser plus integrator. The dependence of the performance on depth of modulation, the number of batches integrated and the photodetection rate is considered for sinusoidal intensity fluctuations. It is demonstrated that improved performance can be achieved with high photodetection rates by using the analogue photomultiplier output rather than photon counting. Finally it is shown that a single frequency can be estimated with an accuracy of about +or-5 kHz from a single batch of 54 photodetections. The implications of this finding for frequency tracking of optical signals are discussed.