There are many variant procedures that all fall under the rubric of LPC. • If the spectral character of the data is time-variable, then it is best not to use a single set of LP coefficients for the whole data set, but rather to partition the data into segments | 572 Chapter 13. Fourier and Spectral Applications There are many variant procedures that all fall under the rubric of LPC. If the spectral character of the data is time-variable then it is best not to use a single set of LP coefficients for the whole data set but rather to partition the data into segments computing and storing different LP coefficients for each segment. If the data are really well characterized by their LP coefficients and you can tolerate some small amount of error then don t bother storing all of the residuals. Just do linear prediction until you are outside of tolerances then reinitialize using M sequential stored residuals and continue predicting. In some applications most notably speech synthesis one cares only about the spectral content of the reconstructed signal not the relative phases. In this case one need not store any starting values at all but only the LP coefficients for each segment of the data. The output is reconstructed by driving these coefficients with initial conditions consisting of all zeros except for one nonzero spike. A speech synthesizer chip may have of order 10 LP coefficients which change perhaps 20 to 50 times per second. Some people believe that it is interesting to analyze a signal by LPC even when the residuals Xj. are not small. The x s are then interpreted as the underlying input signal which when filtered through the all-poles filter defined by the LP coefficients see produces the observed output signal. LPC reveals simultaneously it is said the nature of the filter and the particular input that is driving it. We are skeptical of these applications the literature however is full of extravagant claims. CITED REFERENCES AND FURTHER READING Childers . ed. 1978 Modern Spectrum Analysis New York IEEE Press especially the paper by J. Makhoul reprinted from Proceedings of the IEEE vol. 63 p. 561 1975 . Burg . 1968 reprinted in Childers 1978. 1 Anderson N. 1974 reprinted in Childers 1978. 2 Cressie N. 1991 in
