Optimal Linear Interpolation Research Articles

Optimal linear interpolation in linear predictive vocoders

In low-bit-rate linear predictive (LP) vocoders, the process of parameter interpolation at the receiver helps in smoothing the roughness in the synthesized speech which is normally associated with infrequent parameter updating. Simple linear interpolation has been used almost exclusively in LP vocoder systems. We propose an optimal linear interpolation scheme that requires the transmission of an extra parameter per frame, α : 0 ⩽ α ⩽ 1. The value of α determines that point along the line used for linear interpolation which minimizes the mean-square error with respect to the actual parameter values at the interpolation point. This, of course, requires the computation of the actual parameter values at the transmitter, but only the value of α need be transmitted. The transmission of α requires on the order of 150 bits/second. Experimental results have shown the proposed interpolation scheme to be superior to simple linear interpolation, especially during rapid transitions in the speech signal.

Error Formulae for Optimal Linear Filtering, Prediction and Interpolation of Stationary Time Series

Several explicit expressions are presented for the minimum mean square error in linear causal filtering, prediction and interpolation of weakly stationary discrete-time processes corrupted by additive noise. A general procedure for deriving error expressions of this kind is established.