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翻訳と辞書　辞書検索 [ 開発暫定版 ] スポンサード リンク Line spectral frequencies ： ウィキペディア英語版 Line spectral pairs Line spectral pairs (LSP) or line spectral frequencies (LSF) are used to represent linear prediction coefficients (LPC) for transmission over a channel. LSPs have several properties (e.g. smaller sensitivity to quantization noise) that make them superior to direct quantization of LPCs. For this reason, LSPs are very useful in speech coding. LSP representation was developed by Fumitada Itakura in the 1970s.〔See e.g. http://www.work.caltech.edu/~ling/pub/icslp98lsp.pdf〕 == Mathematical foundation == The LP polynomial $A(z)\; =\; 1-\; \backslash sum\_^p\; a\_k\; z^$ can be expressed as $A(z)\; =\; 0.5(+\; Q(z))$, where: * $P(z)\; =\; A(z)\; +\; z^A(z^)$ * $Q(z)\; =\; A(z)\; -\; z^A(z^)$ By construction, ''P'' is a palindromic polynomial and ''Q'' an antipalindromic polynomial; physically ''P''(''z'') corresponds to the vocal tract with the glottis closed and ''Q''(''z'') with the glottis open.〔http://svr-www.eng.cam.ac.uk/~ajr/SpeechAnalysis/node51.html#SECTION000713000000000000000 Tony Robinson: Speech Analysis〕 It can be shown that: * The roots of ''P'' and ''Q'' lie on the unit circle in the complex plane. * The roots of ''P'' alternate with those of ''Q'' as we travel around the circle. * As the coefficients of ''P'' and ''Q'' are real, the roots occur in conjugate pairs The Line Spectral Pair representation of the LP polynomial consists simply of the location of the roots of ''P'' and ''Q'' (i.e. $\backslash omega$ such that $z\; =\; e^,\; P(z)\; =\; 0$). As they occur in pairs, only half of the actual roots (conventionally between 0 and $\backslash pi$) need be transmitted. The total number of coefficients for both ''P'' and ''Q'' is therefore equal to ''p'', the number of original LP coefficients (not counting $a\_0=1$). A common algorithm for finding these〔e.g. lsf.c in http://www.ietf.org/rfc/rfc3951.txt〕 is to evaluate the polynomial at a sequence of closely spaced around the unit circle, observing when the result changes sign; when it does a root must lie between the points tested. Because the roots of ''P'' are interspersed with those of ''Q'' a single pass is sufficient to find the roots of both polynomials. To convert back to LPCs, we need to evaluate $A(z)\; =\; 0.5(Q(z))$ by "clocking" an impulse through it ''N'' times (order of the filter), yielding the original filter, ''A''(''z''). 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Line spectral pairs」の詳細全文を読む スポンサード リンク 翻訳と辞書 : 翻訳のためのインターネットリソース Copyright(C) kotoba.ne.jp 1997-2016. All Rights Reserved.