In the paper a method is presented for the removal of impulsive disturbances from noisy speech and musical signals. The algorithm is based on a detection-interpolation scheme. The design of the impulsive noise detector subsystem is motivated by the observation that linear prediction systems are quite adequate for the modelling of speech signals whereas they can not model impulsive disturbances. It is shown that transforming the speech signal to the glottal excitation may result in significant reduction of the scale of the speech signal to almost that of the excitation signal whereas the scale of impulsive noise does not decrease. This can lead to a significant improvement in the detectability of the noise pulses. Further improvement may be obtained by the application of a matched filter to the noisy excitation signal. The signal samples that are obliterated by impulsive noise are discarded and interpolated. The interpolation method produces a least squared error estimate of the missing samples using speech samples in the vicinity of the missing block and an estimate of the LPC model of the signal. It is shown that the performance of the interpolation system improves significantly when the LPC model incorporates long term correlation structure in addition to the usual short term correlation parameters.