Zero modeling error (ZME) at the meeting point of LPC and SVD analysis

The frequency analysis of a signal is considered. Although the classical approach based on the representation of a signal in terms of complex exponentials has its merit, an alternative approach aiming to represent a signal by a sum of exponential functions is also interesting. An exact solution to this problem is found at the meeting point of linear predictive coding (LPC) and modeling techniques based on the singular value decomposition (SVD) analysis. Further insight in the structural analysis of a signal is provided. The rank of a signal is defined, and it is shown that full recovery of finite rank data from an incomplete set is always possible