In this paper two aspects of Line Spectrum Pair (LSP) representation of speech are investigated: the method of converting Linear Predictive Coding (LPC) coefficients to LSP frequencies and the relationships between LPC spectrum and LSP frequencies. A new approach to LSP extraction is proposed which exploits the interframe redundancy of LSP frequencies in order to ensure, on the average, a low computational complexity. Some spectral properties of the LSP frequencies are then described. Starting from these properties, an LSP-based distance measure is introduced which approximates the rms log spectral measure and can be easily evaluated in parallel with the extraction procedure, in order to obtain a preliminary segmentation of speech.