Section: Application Domains

Signal Processing

Applications of sequential learning in the field of signal processing are also very numerous. A signal is naturally sequential as it flows. It usually comes from the recording of the output of sensors but the recording of any sequence of numbers may be considered as a signal like the stock-exchange rates evolution with respect to time and/or place, the number of consumers at a mall entrance or the number of connections to a web site. Signal processing has several objectives: predict , estimate, remove noise, characterize or classify. The signal is often considered as sequential: we want to predict, estimate or classify a value (or a feature) at time $t$ knowing the past values of the parameter of interest or past values of data related to this parameter. This is typically the case in estimation processes arising in dynamical systems.

Signals may be processed in several ways. One of the best–known way is the time-frequency analysis in which the frequencies of each signal are analyzed with respect to time. This concept has been generalized to the time-scale analysis obtained by a wavelet transform. Both analysis are based on the projection of the original signal onto a well-chosen function basis. Signal processing is also closely related to the probability field as the uncertainty inherent to many signals leads to consider them as stochastic processes: the Bayesian framework is actually one of the main frameworks within which signals are processed for many purposes. It is worth noting that Bayesian analysis can be used jointly with a time-frequency or a wavelet analysis. However, alternatives like belief functions came up these last years. Belief functions were introduced by Demspter few decades ago and have been successfully used in the few past years in fields where probability had, during many years, no alternatives like in classification. Belief functions can be viewed as a generalization of probabilities which can capture both imprecision and uncertainty. Belief functions are also closely related to data fusion.