A Modified Prony Algorithm for Estimating Sinusoidal Frequencies
نویسنده
چکیده
We investigate the modified Prony algorithm of Osborne and Smyth (1991, 1993) applied to the estimation of the frequency of oscillation of a sinusoidal signal with added white noise, and compare it with the algorithms usually associated with the names of Prony and Pisarenko. We show that the Pisarenko algorithm returns O(N− 1 2 ) consistent estimates, and that the modified Prony algorithm returns the least squares estimates which are O(N− 3 2 ) consistent. The transfer function parameter estimates that are returned by these algorithms converge to the true values at the same rate as the frequency estimates in each case. A concise expressions for the asymptotic covariance matrix of these estimates is given in the simplest case. Small sample properties, starting values and the importance of correctly specifying the number of sinusoids, are investigated in a simulation study.
منابع مشابه
Speech analysis by subspace methods of spectral line estimation
Over frames of short time duration, filtered speech may be described as a finite linear combination of sinusoidal components. In the case of a frame of voiced speech the frequencies are considered to be harmonics of a fundamental frequency. It can be assumed further that the speech samples are observed in additive white noise of zero mean, resulting in a standard signal-plus-noise model. This m...
متن کاملAdaptive Notch Iir Filters
Notch filters represent a method of estimating and/or tracking sinusoidal frequencies immerged in background noise. We shall refer to adaptive notch IIR filters, which make use of the RLS method. This paper presents an implementation of adaptive notch IIR filters on MOTOROLA StarCore140 DSP. We have used a modified RLS algorithm, more suitable for DSP implementation. The paper presents theoreti...
متن کاملImproving Sinusoidal Frequency Estimation Using a Trigonometric Approach
Estimating the frequency of sinusoidal components is the first part of the sinusoidal analysis chain. Among numerous frequency estimators presented in the literature, we propose to study an estimator proposed in [1] known as the derivative algorithm. Thanks to a trigonometric interpretation of this frequency estimator, we are able to propose a new estimator which improves estimation performance...
متن کاملA Modified Prony Algorithm for Fitting Functions Defined by Difference Equations
This paper reformulates, generalizes and investigates the stability of the modified Prony algorithm introduced by Osborne (1975), with special reference to rational and exponential fitting. The algorithm, originally for exponential functions, is generalized to the least squares fitting of any function which satisfies a linear homogeneous difference equation. Using the difference equation formul...
متن کاملA Prony Approach to Modeling of Time-Varying Fuzzy Systems
This paper extends the Prony method to the identification of a class of fuzzy systems parameterized by a set of time-varying parameters. The Prony formulation is an optimal solution minimizing the fluctuation effects while accurately estimating the time-varying system parameters. A closed-form and efficient algorithm for adaptively calculating the time-varying parameters is derived. This soluti...
متن کامل