Discrete H∞ filter design with application to speech enhancement

Discrete H_∞ filter design with a linear quadratic (LQ) game approach is presented. The exogenous inputs composed of the “hostile” noise signals and system initial condition are assumed to be finite energy signals with unknown statistics. The design criterion is to minimize the worst possible amplification of the estimation error signal, which is different from the classical minimum variance estimation error criterion for the modified Wiener or Kalman filter design. The approach can show how far the estimation error can be reduced under an existence condition on the solution to a corresponding Riccati equation. The application of the discrete H_∞ filter to enhance speech contaminated by additive noise is then investigated. In the H_∞ estimation, the noise sources can be arbitrary signals with only the requirement of bounded energy, this estimation is more appropriate in practical speech enhancement