Hierarchical descriptors for nonstationary 1 and 2 dimensional signal processing
Andrew D. Calway, Roland Wilson · Warwick Research Archive Portal (University of Warwick) · 1987
The representation of signals with important local properties is considered. These signals have a degree of nonstationarity which is dependent upon the amount of localisation. Signal descriptors which seek to represent such signals must correspond in scale to the local properties in order to provide an efficient representation. A review is given of various methods that have been adopted. Although some of these have been used in specific applications, a general and computationally efficient representation is not available. A new descriptor is presented which seeks to fulfil this requirement. It combines the time and frequency representations of a signal in an optimal way by using basis functions which are maximally concentrated in both domains. This corresponds to representing the local properties of the signal. The descriptor adopts a hierarchical structure which incorporates multi-resolution in both domains so that the required amount of localisation can be determined for a given signal. This enables the descriptor to be generally applied since it is consistent with the concept of a nonstationary signal. Results of initial experiments on the descriptor are presented and the report concludes with a discussion of future investigations.