The properties and applications of morphological filters for speech analysis are investigated. We introduce and investigate a novel nonlinear spectral envelope estimation method based on morphological operations, which is found to be very robust against noise. This method is also compared with the spectral envelope estimation vocoder (SEEVOC) method. A simple method for the optimum selection of the structuring set size without using pitch information is proposed. Also, a new concept of higher order peaks is introduced and found to be beneficial. The morphological approach is then used for a new pitch estimation method. The harmonic-plus-noise decomposition is used to develop a novel and flexible noise reduction method.