A new eigenstructure method for sinusoidal signal retrieval in white noise: estimation and pattern recognition

A new approach, in a framework of an eigenstructure method using a Hankel matrix, is developed for sinusoidal signal retrieval in white noise. A closed-form solution for the singular pairs of the matrix is defined in terms of the associated sinusoidal signals and noise. The estimated sinusoidal singular vectors are applied to form the noise-free Hankel matrix. A pattern recognition technique is proposed for partitioning signal and noise subspaces based on the singular pairs of the Hankel matrix. Three types of cluster structures in an eigen-spectrum plot are identified: well-separated, touching, and overlapping. The overlapping, which is the most difficult case, corresponds to a low signal-to-noise ratio (SNR). Optimization of Hankel matrix dimensions is suggested for enhancing separability of cluster structures. Once features have been extracted from both singular value and singular vector data, a fuzzy classifier is used to identify each singular component. Computer simulations have shown that the method is effective for the case of “touching” data and provides reasonably good results for a sinusoidal signal reconstruction in the time domain. The limitations of the method are also discussed.