Abstract
A novel adaptive FIR filter for the estimation of a single-tone sinusoid corrupted by additive noise is described. The filter is based on an offline optimization procedure which, for a given notch frequency, computes the filter coefficients such that the frequency response is unity at that frequency and a weighted noise gain is minimized. A set of such coefficients is obtained for notch frequencies chosen at regular intervals in a given range. The filter coefficients corresponding to any frequency in the range are computed using an interpolation scheme. An adaptation algorithm is developed so that the filter tracks the sinusoid of unknown frequency. The algorithm first estimates the frequency of the sinusoid and then updates the filter coefficients using this estimate. An application of the algorithm to beamforming is included for angle-of-arrival estimation. Simulation results are presented for a sinusoid in correlated noise, and compared with those for the adaptive IIR notch filter.
Highlights
Estimation of sinusoidal signals and their frequencies from noisy measurements is important in many fields such as angle of arrival estimation, frequency-shift keying (FSK) demodulation, Doppler estimation of radar waveforms, biomedical engineering, sensor array processing, and cancellation of periodic interferences [1]
A new adaptive notch FIR filter is introduced. This filter has the novel feature that its frequency responses can be optimized in an offline manner
Unlike the IIR filter, the adaptive FIR filter is always stable for θs θs suitable choice of stepsizes
Summary
Estimation of sinusoidal signals and their frequencies from noisy measurements is important in many fields such as angle of arrival estimation, frequency-shift keying (FSK) demodulation, Doppler estimation of radar waveforms, biomedical engineering, sensor array processing, and cancellation of periodic interferences [1]. The filter coefficients are adapted to track the input signal by using filter coefficients stored at preselected frequencies in the range [0, π] In this way, an adaptive FIR notch filter with frequency responses optimized to reject correlated noise is obtained. An adaptive FIR notch filter with frequency responses optimized to reject correlated noise is obtained This approach resembles that of [10] which employs online constraints for waveform estimation in the frequency domain. It is shown that the proposed filter provides performance gains compared with the adaptive IIR notch filter in terms of signal and frequency estimation, at frequencies outside of the noise band. EURASIP Journal on Applied Signal Processing techniques) It can be successfully employed in adaptive beamforming applications [2], where interference in certain directions can be effectively suppressed.
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