Speech coding using the matrix pencil

Matrix Pencils (MP) facilitate the study of differential equations resulting from oscillating systems. Certain problems in linear ordinary differential equations, such as speech processing, can be represented as the problem of finding a canonical pencil strictly equivalent to a given pencil. The MP is a direct data domain approach to estimate the signal's poles. The MP depends on only the data and is not a stochastic estimator. This approach has many benefits over a statistical approach. One benefit is that a smaller amount of data could be used to estimate the poles. The second benefit is that it results in a lower variance associated with the estimates of the parameters, which comes close to the Cramer-Rao bound [1]. In this paper, the results of recent work have been extended [2].