Cepstral domain interpretations of line spectral frequencies

In this paper, we derive a relationship between a linear prediction (LP) polynomial and its corresponding line spectral frequencies (LSFs) in cepstral domain. We first obtain the cepstral representations of the symmetric and the antisymmetric polynomials constructed from the LP polynomial. The sum of these cepstra corresponds to the pseudo-cepstrum [H.K. Kim, S.H. Choi, H.S. Lee, On approximating line spectral frequencies to LPC cepstral coefficients, IEEE Trans. Acoust. Speech Audio Process. 8(2) (2000) 195–199]. Finally, LSFs can be computed by matching these two cepstra. Additionally, we derive the recursive relations between LSFs and the LPC coefficients, as well as between LSFs and LPC cepstral coefficients.