Statistics : Statistical Signal Processing

Signal processing may broadly be considered to involve the recovery of information from physical observations. The received signals are usually disturbed by thermal, electrical, atmospheric or intentional interferences. Due to the random nature of the signal, statistical techniques play an important role in signal processing. Statistics is used in the formulation of appropriate models to describe the behaviour of the system, the development of appropriate techniques for estimation of model parameters, and the assessment of model performances. Statistical Signal Processing basically refers to the analysis of random signals using appropriate statistical techniques. Different one and multidimensional models have been used in analyzing various one and multidimensional signals. For example ECG and EEG signals, or different grey and white or colour textures can be modelled quite effectively, using different non-linear models. Effective modelling are very important for compression as well as for prediction purposes. The important issues are to develop efficient estimation procedures and to study their properties. Due to non-linearity, finite sample properties of the estimators cannot be derived; most of the results are asymptotic in nature. Extensive Monte Carlo simulations are generally used to study the finite sample behaviour of the different estimators.