# Duality theory of composite sinusoidal modeling and linear prediction

@article{Sagayama1986DualityTO, title={Duality theory of composite sinusoidal modeling and linear prediction}, author={Shigeki Sagayama and Fumitada Itakura}, journal={ICASSP '86. IEEE International Conference on Acoustics, Speech, and Signal Processing}, year={1986}, volume={11}, pages={1261-1264} }

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 variablesz = e^{j\omega}(LPC) andx = \cos\omega(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…

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