In many still-image and video processing applications, the time-frequency localization properties of the decomposition technique are an important consideration. While bandwidth compression of the image requires operators with good localization in frequency, spatial features such as edge preservation demand a high degree of localization in time (or the spatial variable). These requirements compete with each other and one is secured at the expense of the other. The classical "uncertainty" principle in the continuous-time domain provides the back drop for this trade-off. Our purpose is to review recent extensions of this principle to the discrete-time case and to develop optimum wave forms. We review common features of block transforms, subband filter banks, and wavelets, and demonstrate how the discrete uncertainty can be used to evaluate these decomposition methods. In particular, we evaluate the trade-off between localization in time and in frequency for several proposed signal decomposition structures.
Richard A. Haddad,
Ali Naci Akansu,
"Time-frequency localization in transforms, subbands, and wavelets: a critical review," Optical Engineering 32(7), (1 July 1993). https://doi.org/10.1117/12.138550