The problem of statistical signal processing is a central topic at the interface of modern statistics and machine learning and is connected to both theoretical and applied parts of these sciences. In this framework, I will present research I have conducted in the fields of statistical modeling and inference with applications to signal processing problems. I will first present hidden process regression models for non-stationary signal approximation and segmentation. I will also consider the problem of modeling non-stationary signals with possibly skewed and heavy tailed non-Gaussian noise. Then, when the basic unit of information is an entire signal, I will present hierarchical dynamical mixtures to simultaneously segment and classify signals, directly in the signal space, in a functional data analysis framework. The problem of bi-dimensional signal (surface) classification is also considered by using Bayesian spatial spline regression mixtures with random effects. Finally, a part of this talk will be on Bayesian non-parametric parsimonious mixtures with an application to the decomposition of humpback whale songs from the Sabiod plateform http://sabiod.univ-tln.fr/