A frequency weighted Itakura-Saito spectral distance measure

A new spectral distance measure is defined by inserting a multiplicative frequency weighting term into the conventional Itakura-Saito measure. When the weighting function is a simple one pole function, then the minimization of the distance between a signal spectrum and an arbitrary N-pole filter results in a set of linear equations that is symmetric and solvable by Cholesky decomposition. When the weighting function is a multiple pole function, the resulting spectral distance minimization produces a set of nonlinear algebraic equations, but fortunately a simple method exists for obtaining an approximate solution which can be refined using the Newton-Raphson method. Results of some preliminary trials in applying the technique to LPC vocoding are described.