The conversion between Immittance Spectral Pairs pseudo-cepstrum and Linear Predictive Coding coefficients

In this paper, we derived a relationship between Linear Predictive Coding (LPC) coefficients and Immittance Spectral Pairs (ISP) pseudo-cepstrum. In Adaptive Multi-Rate Wideband (AMR-WB) speech codec, ISP parameters were used for quantisation and interpolation. This paper first described the representation of ISP pseudo-cepstrum. ISP pseudo-cepstrum was defined as the inverse z-transform of half natural logarithm of immittance function. References [2] and [3] proposed two kinds of new perceptual weighting filters based on ISP pseudo-cepstrum. Spectral tilt is more pronounced in wideband signals due to the wide dynamic range between low and high frequencies. The proposed filters are helpful for solving this problem. Then we gave the conversion method between ISP pseudo-cepstrum and polynomials cepstrum coefficients. Finally we derived the recursive relations between ISP pseudo-cepstrum and LPC coefficients. There are two methods of converting LPC coefficients to ISP pseudo-cepstrum. The one is directly from LPC coefficients to ISP pseudo-cepstrum. The other is from ISP parameters.