Most narrowband CELP-based speech coders (such as AMR-NB) use Itakura's line spectral pair (LSP) representation of LP parameters. However, there is another representation, proposed by Bistritz, called immittance spectral pair (ISP) which has been used in AMR-WB. From what I gather, ISPs and LSPs are related, where for order m, the first m-1 ISPs are the LSFs for order m-1, and the mth ISP is the last linear predictive coefficient.

Anyway, assuming I haven't made any error in adapting the ISP routines from the AMR-WB, I find that, in terms of log spectral distortion, that quantising ISPs gives worser performance (0.2 dB) than quantising LSPs, for the same bitrate. This might be accounted for by the quantising scheme I'm using (GMM-based) but I'm not certain.

It often makes me wonder what the reasons were for going with ISPs in AMR-WB rather than LSPs which have been studied for so many years in narrowband speech coding. Any ideas?

AFAIK, the main reason is political, not technical. As for quantization results, I've heard that ISP could produce slightly better results, but I haven't tried. Note that the result probably depend on how you quantize the last parameter, which has a different interpretation. If you're using VQ on the whole ISP vector, try applying a gain to the last parameter (smaller or larger than 1) and see what happens.

Thanks for the information. In Bistritz' paper, he shows in scalar quantization experiments that ISPs give slightly less spectral distortion than LSPs (and a little less outliers too). But there don't seem to be that many studies in the literature comparing the two. Again, many thanks.