Influence of the noise on DFT-based sine-wave frequency and amplitude estimators

This paper analyses the effect of wide-band noise on the accuracy of generic sine-wave frequency and amplitude estimators based on Discrete Fourier Transform (DFT) samples located closely to the spectrum peak. A cosine window is adopted to reduce the influence on the estimated parameters of spectral leakage from the negative frequency component. Closed-form expressions for the estimator variances are derived. Moreover, the variance of a frequency estimator expressed as a ratio of generic linear functions of DFT sample modules is specifically investigated. It is also shown that the same frequency estimation accuracy can be achieved when complex-valued DFT samples are considered. The derived expressions are verified on a specific sine-wave frequency estimator and a related amplitude estimator, using both simulation and experimental results.