This thesis presents a new robust filtering technique that suppresses impulsive noise in speech signals. The method makes use of Projection Statistics based on medians to detect segments of speech with impulses. The autoregressive model employed to smooth out the speech signal is identified by means of a robust nonlinear estimator known as the Schweppe-type Huber GM-estimator. Simulation results are presented that demonstrate the effectiveness of the filter. Another contribution of the work is the development of a robust version of the Kalman filter based on the Huber M-estimator. The performances of this filter are evaluated for a simple autoregressive process.