Duality theory of composite sinusoidal modeling and linear prediction

This paper reveals that an elegant duality exists between Linear Prediction (LPC) and Composite Sinusoidal Modeling (CSM) from the viewpoint of orthogonal polynomial theory. Both LPC and CSM are formulated as orthogonal polynomial theory with variables (LPC) and (CSM) where the "inner product" is defined by the integral of a pair of functions of frequency ω weighted by the spectral density function of the signal. This viewpoint leads to the duality of LPC and CSM and reveals the correspondence between parameters in the LPC and CSM domains. Conventional LPC theory (including PARCOR) is shown to explain only half of the theory presented here. The theory of mutual conversion between LPC and CSM yields a new interpretation of LSP (line spectrum pairs) and an alternative algorithm for LSP analysis. Fundamental properties of LSP are derived.