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Speech is a continuous signal, which means that consecutive samples of the signal are correlated (see figure on the right). In particular, if we know a previous sample xn-1, we can make a prediction of the current sample, \( \hat x_n = x_{n-1}, \) such that \( \hat x_n \approx x_n. \) By using more previous samples we have more information, which should help us make a better prediction. Specifically, we can define a predictor which uses M previous samples to predict the current sample xas

\[ \hat x_n = - \sum_{k=1}^M a_k x_{n-k}. \]

A short segment of speech

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