less than one (Section 4.4). In practice, however, there are situations under which stability can be threatened. For instance, under marginally stable conditions, the limited precision of the computational environment can lead to errors high enough to produce an unstable filter; this could happen for signals with sustained oscillation, where the spectrum is associated with poles close to the unit circle. In this section we study several techniques employed in speech coding to fix the described problem, all of them aimed at alleviating ill-conditioning during LP analysis and, at the same time, improving the stability of the resultant synthesis filter, as well as the quality of the synthetic speech. These techniques can be used in an isolated fashion or combined together.Pre-emphasis of the Speech WaveformThe typical spectral envelope of the speech signal has a high frequency roll-off due to radiation effects of the sound from the lips. Hence, high-frequency components have relatively low amplitude, which increases the dynamic range of the speech spectrum. As a result, LP analysis requires high computational precision to capture the features at the high end of the spectrum. More importantly, when these features are very small, the correlation matrix can become ill-conditioned and even singular, leading to computational problems. One simple solution is to process the speech signal using the filter with system function
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