Line spectral pairs (LSP) or line spectral frequencies (LSF) are used to represent linear prediction coefficients (LPC) for transmission over a channel.
LSP representation was developed by Fumitada Itakura,[2] at Nippon Telegraph and Telephone (NTT) in 1975.
[3] From 1975 to 1981, he studied problems in speech analysis and synthesis based on the LSP method.
[4] In 1980, his team developed an LSP-based speech synthesizer chip.
LSP is an important technology for speech synthesis and coding, and in the 1990s was adopted by almost all international speech coding standards as an essential component, contributing to the enhancement of digital speech communication over mobile channels and the internet worldwide.
[3] LSPs are used in the code-excited linear prediction (CELP) algorithm, developed by Bishnu S. Atal and Manfred R. Schroeder in 1985.
[5] It can be shown that: The Line Spectral Pair representation of the LP polynomial consists simply of the location of the roots of P and Q (i.e.
As they occur in pairs, only half of the actual roots (conventionally between 0 and
A common algorithm for finding these[6] is to evaluate the polynomial at a sequence of closely spaced points around the unit circle, observing when the result changes sign; when it does a root must lie between the points tested.
Moreover, the closer two roots are, the more resonant the filter is at the corresponding frequency.
Because LSPs are not overly sensitive to quantization noise and stability is easily ensured, LSP are widely used for quantizing LPC filters.