Efficient Iterative Frequency Estimator of Sinusoidal Signal in Noise

Abstract

The frequency estimation of the sinusoidal signal in noise is a problem of prime importance. A usual estimation method uses the Discrete Fourier transform to obtain the coarse estimation which is improved by a fine estimation stage. In this paper, we propose an efficient iterative estimation algorithm using the phase shift Fourier interpolation. We derive the performance of the new estimator. We show that the estimator is asymptotically unbiased and its mean squared error is slightly above the asymptotical Cramer-Rao bound over the whole frequency estimation range. To reduce the calculation, we study the estimation errors of the coarse estimation caused by finite data bits and short signal sequence. An approximate model is proposed by which we can obtain the estimation errors of different data bits and sequence length. Then we choose the proper sequence length and data bits to achieve the coarse search. This allows for a dramatic reduction in the calculation of coarse estimation, while still attaining the same performance comparable to that of a full length and data bits. In the numerical results we show that, in the proposed framework, when the signal to noise ratio is bigger than 11 dB, the computation speed is 13.45 times of the original with 512 sampling points.