Immittance Spectral Pairs (isp) for Speech Encoding

Immittance Spectral Pairs (ISP) form a new set of parameters proposed for presenting the LPC filter. ISP is close to LSP and owns similar ‘niceties’, yet it is different. For a filter of order n it consists of a ‘gain’ and n-1 ‘frequency’ parameters instead of n ‘frequency’ parameters for LSP. In regarding LPC as a pseudo model for the vocal tract ISP may represent the immittance at the glottis, without posing, like LSP, artificial boundary conditions. In quantization experiments, ISP has been found to compare favorably with LSP. A study of interframe differentiation coding for ISP and LSP is included and it demonstrates the respectives performances of the two sets. 1. Immittance Spectral Pairs The LPC filter l / A p ( z ) is realizable by a cascade of p lattice sections that implement the following Levinson recursions for n = 1,. . . , p , with Afj(z) := z-”A,,(z-’> A,,(z) = A,l ( z ) k,,z-lA:-l(a) (la) A i ( z ) = -k,,A,,-l(z) + ~ l A t \ ~ ( z ) (lb) This scheme can also be understood as a pseudo model for the vocal tract that consist of p lossless sections of different immittances counted from the lips to the glottis with A,,, A i and k,, representing, respectively, wave moving forward, backward in section n and the amount of A,, that is reflected at the boundary (e.g. It is possible, however, to replace in the Levinson and other related algorithms the forward and backward variables, the so called “scattering” variables by their sums and differences PI). Fn(2) = A , ( 4 + A i ( z ) ; Gn(2) = A,(z)-A11(4 (2) called “immittance” variables (as they may represent the wave field variables sound pressure and volume v e locity in the current context, whose ratios are impedance This Work was partly supported by the UNITED STATES -ISRAEL BSF under Grant No. 88-425. or admittance) and obtain alternative (and more efficient) immittance variable versions to these algorithms If the model for the vocal tract is reformulated into immittance variables the input immittance of the model (the immittance at the glottis) becomes [4], ~ 3 1 .