A new prony-based circular-hyperbolic decomposition

We introduce a new closed-form decomposition technique for estimating the m odel parameters of an evenly sampled signal known to be composed of circula r and hyperbolic sine and cosine functions in the presence of Gaussian whit e noise. The techniqe is closely related to Prony's method and hereditary a lgorithms that fit complex exponential functions to evenly sampled data. Th e circular and hyperbolic sine and cosine Functions are obtained by adding constraints that limit the form of the characteristic polynomial coefficien ts. It avoids the leakage effects associated with the discrete fourier tran sform (DFT) for circular sine and cosine functions. When the signal contain s frequency components that are not rational multiples of each other, the p roposed decomposition yields amplitude and phase parameters that are more a ccurate than those obtained with the DFT in moderate levels of noise. First , we review Prony's method and one hereditary algorithm (the complex expone ntial algorithm). Then, we detail three implementation procedures of the ne w technique. The first is a two-stage least-squares approach. The second ut ilises a novel concept of noise reduction which is attributed to Pisarenko. The last provides additional means of noise reduction through a covariance formulation that avoids zero-lag terms. Experimental and numerical example s of the application of the circular-hyperbolic decomposition (CHD) are giv en. (C) 2001 Academic Press.