Estimation of the frequency and waveform of a single-tone sinusoid using an offline-optimized adaptive filter

A novel offline-optimized adaptive filtering (OOAF) algorithm is proposed which allows the coupled estimation of waveform and frequency of a single-tone sinusoid in additive Gaussian noise. In a specified range of frequencies, the coefficients of an FIR filter are computed to minimize a given noise power. At a particular frequency in the range, quadratic polynomials are used to compute the impulse response and its derivative with respect to frequency. The waveform and its frequency are then determined by an adaptive algorithm that uses the offline-optimized filter. In AWGN, the frequency estimate is shown to be unbiased and has an approximate asymptotic variance derived analytically. Simulation and analytical results show that OOAF exhibits excellent performance in tracking the sinusoidal waveform and estimation of its frequency, especially in colored noise.