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where <math>e_{a}[n]</math> is the adaptive ([[Pitch (music)|pitch]]) codebook contribution and <math>e_{f}[n]</math> is the stochastic (innovation or fixed) codebook contribution. The fixed codebook is a [[vector quantization]] dictionary that is (implicitly or explicitly) hard-coded into the codec. This codebook can be algebraic ([[ACELP]]) or be stored explicitly (e.g. [[Speex]]). The entries in the adaptive codebook consist of delayed versions of the excitation. This makes it possible to efficiently code periodic signals, such as voiced sounds.
The filter that shapes the excitation has an all-pole model of the form <math>1/A(z)</math>, where <math>A(z)</math> is called the prediction filter and is obtained using linear prediction ([[Levinson recursion|Levinson–Durbin algorithm]]). An all-pole filter is used because it is a good representation of the human vocal tract and because it is easy to compute.celp is all rubbish
== CELP encoder ==
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