CLOSED-FORM FREQUENCY ESTIMATION USING SECOND-ORDER NOTCH FILTERS

In this paper the problem of the frequency estimation of a sinusoid embedded in white noise is considered. The approach used herein is the minimization of the sample variance of the output of constrained notch filters fed by the noisy sinusoid. In particular, this paper focuses on closed-form expressions of the frequency estimate, which can be obtained using notch filters having an all-zeros FIR structure. In this paper it is shown that the FIR notch filters obtained from standard 2nd-order IIR filters are inadequate, and an alternate 2nd-order IIR notch filter is proposed, which provides an unbiased estimate of the frequency. The FIR filter obtained from the new IIR filter provides a closed-form unbiased frequency estimate.