A time domain reformulation of linear prediction equivalent to the LSP decomposition

The Line spectrum pair (LSP) decomposition is a widely used method in speech coding. In this paper, we will present a reformulation of conventional linear prediction which is equivalent to the LSP decomposition. The paper shows that the symmetric and antisymmetric polynomials of the LSP decomposition are equivalent to two filters, that are determined by predicting a signal sample using its averaged and differentiated previous values.