Optimizing time-frequency resolution of orthonormal wavelets

The authors consider the time and the frequency resolutions associated with the wavelet transform since these resolution properties are essential to evaluate a time-frequency analysis tool. A method is introduced to measure the resolution properties of the orthonormal wavelets. The authors exploit the degree of freedom in the construction of compactly supported wavelets in order to find the ones which yield the highest time-frequency concentration. It is shown that some of these orthonormal wavelets get close to the Heisenberg limit, which makes the corresponding wavelet transform particularly appropriate to signal analysis