In the previous chapter, a number of linear prediction formulations were developed Although different formulations may have appeared to be specifying different problems, it was shown that they all led to the same problem, that of minimizing an expression of the form

wherea₀ = 1, or equivalently, solving the simultaneous equations

for the coefficientsa_i. The coefficientsc_ij were obtained from a correlation of the input data sequence

.In the PARCOR approach of Section 2.6,α,c_ij, anda_i do not explicitly appear, but thea_i terms are implicit in the PARCOR lattice since the overall structure definesA (z). In addition,α of (3.1) is minimized by the PARCOR approach, for it is identical toα_M of (2.47).

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Authors and Affiliations

1. Speech Communications Research Laboratory, Inc., 93109, Santa Barbara, California, USA

   John D. Markel & Augustine H. Gray Jr.

2. Department of Electrical Engineering and Computer Science, University of California Santa Barbara, 93106, California, USA

   Augustine H. Gray Jr.

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