Sinusoidal Frequency Estimation Research Articles

Asymptotic zero distribution of orthogonal polynomials in sinusoidal frequency estimation

It is shown that the zeros of polynomials orthogonal with respect to certain positive measures on the unit circle have an asymptotic distribution which is uniform on a circle of radius less than or equal to one. These results explain some phenomena observed when various linear prediction methods are used to estimate sinusoidal frequencies. They also describe the asymptotic zero distribution of the prediction error filter polynomials for a class of time series including autoregressive moving average (ARMA) models.

An adaptive IIR structure for sinusoidal enhancement, frequency estimation, and detection

An adaptive IIR structure for processing a sinusoidal signal in broad-band noise is introduced. The structure contains three adaptive processors, each of which is computationally very simple. Useful features of the structure include enhancement, frequency estimation, and detection.

Accurate frequency estimation at low signal-to-noise ratio

A frequency estimator for sinusoids in white noise is described. Convergence results are obtained for the single sinusoid case and a simulation described for the multiple sinusoid case. The estimator is shown to be capable of providing accurate frequency estimates at lower SNR's than currently existing techniques. Furthermore, the simplicity of the algorithm lends itself to a simple and efficient implementation.

Statistical analysis of Pisarenko's method for sinusoidal frequency estimation

Statistical analysis is performed for Pisarenko's method of sinusoidal frequency estimation by using the periodogram technique. Under the assumption that the data consist of several sinusoids plus white noise, we give an asymptotic expression of the error variance of the sinusoidal frequency estimator. Also, a modified method is proposed. This is computationally efficient but the statistical property is not improved. We also present simulation results and compare them to the theoretical ones. Lastly, we point out that the Pisarenko's method can be implemented as an (on-line) bias compensated least-squares algorithm, thus avoiding the eigenvalue and eigenvector calculations.