Prony-based circular-hyperbolic decomposition

S. O.F. Fahey, B. M. Suleiman, A. H. Nayfeh, M. R. Hajj

Research output: Contribution to journalConference articlepeer-review

Abstract

We introduce a new closed-form decomposition technique for estimating the model parameters of an evenly sampled signal known to be composed of circular and hyperbolic sine and cosine functions in the presence of Gaussian noise. The technique is closely related to Prony's method and hereditary algorithms that fit complex exponential functions to evenly sampled data. It also has advantages over the Discrete Fourier Transform (DFT). When the signal contains frequency components that are not integer multiples of each other, the proposed decomposition yields amplitude and phase parameters that are more accurate than those obtained with the DFT. The circular and hyperbolic sine and cosine functions are obtained by adding constraints limiting the poles on the z-plane to the unit circle and real line. First, we review Prony's method and one hereditary algorithm (the complex exponential algorithm). Then, we detail three implementation procedures of the new technique. The first is a two-stage least-squares approach. The second utilizes a novel concept of noise reduction attributed to Pisarenko. The last provides additional means of noise reduction through a covariance formulation that avoids zero-lag terms. Experimental and numerical examples of the application of the circular-hyperbolic decomposition are provided.

Original languageEnglish
Pages (from-to)I/-
JournalProceedings of SPIE - The International Society for Optical Engineering
Volume4062
StatePublished - 2000
EventIMAC-XVIII: A Conference on Structural Dynamics 'Computational Challenges in Structural Dynamics' - San Antonio, TX, USA
Duration: 7 Feb 200010 Feb 2000

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