LPC/SVD analysis of signals with zero modeling error

Abstract The frequency analysis of a signal is reconsidered in this paper. 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 can be found at the meeting point of LPC and SVD analysis. Moreover, an optimal representation in the frequency domain can be obtained offering the possibility of an inverse transform when the original signal has to be recomputed. Further insight in the structural analysis of a signal is provided. The rank of a signal is defined and it is shown that it can only be affected by the frequency and the damping factor of an exponential sinusoid.