Estimation of Two Sinusoids in a Very Short Signal
Rafał Rytel-Andrianik · International Journal of Electronics and Telecommunications · 2012
Estimation of Two Sinusoids in a Very Short Signal In the paper, the estimation of the parameters (frequency, amplitude, phase) of two complex-valued sinusoids embedded in a white gaussian circular additive noise is considered. In this context, it is answered what is the minimal necessary number of signal samples needed to reliably estimate all the parameters of both sinusoids. The Cramer-Rao bounds and maximum likelihood estimator are used in the analysis. The answer to the posed question is not straightforward. It is shown that three signal samples are enough only if the difference of phases between both sinusoids meets certain condition, otherwise estimation results are ambiguous. The use of four signal samples has the advantage that reliable estimates can be obtained irrespectively of this phase difference.