window approach. The use of such a window encapsulates the constraint in many data streaming applications that there is only a limited data storage and memory with which to perform analysis.

Our online dynamic classification technique proceeds as follows. For a window of length $w=2^{J}$ the first step of our algorithm is to calculate the set of discriminative indices as defined in Equation  using a set of training signals of length $w$. For reasons of efficiency, the discriminative indices are used in the classification step for each window of the data. Although window-specific indices could be used, in our experience, updating the set of discriminative indices for each window increases computational complexity without providing significant accuracy improvement. The dynamic classification method described in Section \[subsec:DC\] is applied to the first window of data to obtain the probability that the signal belongs to a particular class for the time points in the window.

Upon arrival of a new data point, the window then shifts by one, and the data under analysis consists of the old data together with the new data point, but we also lose the first data point contained in the previous window. The online wavelet transform is then 