Line spectrum pair (LSP) and speech data compression

TLDR

Line Spectrum Pair (LSP) representation, introduced by Itakura, offers LPC spectral properties such as unit‑circle zeros, interlaced symmetric/antisymmetric zeros, and preservation of minimum‑phase filtering when quantized. This study demonstrates that these LSP properties can be proven using a phase‑function approach. We analyze LSP frequency statistics from a speech database and derive a spectral‑sensitivity expression for single‑frequency deviations to assess quantization effects. The results show that multi‑pulse LPC employing LSP achieves effective spectral information compression.

Abstract

Line Spectrum Pair (LSP) was first introduced by Itakura [1,2] as an alternative LPC spectral representations. It was found that this new representation has such interesting properties as (1) all zeros of LSP polynomials are on the unit circle, (2) the corresponding zeros of the symmetric and anti-symmetric LSP polynomials are interlaced, and (3) the reconstructed LPC all-pole filter preserves its minimum phase property if (1) and (2) are kept intact through a quantization procedure. In this paper we prove all these properties via a "phase function." The statistical characteristics of LSP frequencies are investigated by analyzing a speech data base. In addition, we derive an expression for spectral sensitivity with respect to single LSP frequency deviation such that some insight on their quantization effects can be obtained. Results on multi-pulse LPC using LSP for spectral information compression are finally presented.