Digital encoding of variable-length vectors with application to pitch extraction and pitch-synchronous speech analysis and synthesis

A series expansion of pitch periods is often suggested in order to reduce the information rate of speech signals. Considering speech signals that are sampled at a constant rate, this may be treated as a linear transformation of random vectors with varying length. For a constant length, it is commonly known how to determine the optimum basis vectors from the covariance matrix of the random vector. In this paper it is shown how to define and estimate a special covariance matrix which allows the determination of basis vectors that are especially suited for the expansion of variable length vectors. This expansion may be considered optimum in the sense that it has most of the favourable properties of the Karhunen-Loève transformation (KL), without being restricted to a fixed dimension of the vector space. The new expansion has been tested successfully on speech material in pitch analysis and pitch-synchronous block quantization.