Minimum duration orthonormal wavelets
Joel M. Morris · Optical Engineering · 1996
The discrete wavelet transform (DWT) is becoming increasingly popular as a powerful tool for signal decomposition techniques, which are important for analyzing nonstationary signals. Recently much emphasis has been placed on the time-frequency resolution properties of wavelets, which involves designing wavelets with good localization in both time and frequency via minimization of the time duration/frequency bandwidth product of the wavelet function. But certain practical applications, such as detection of edges in an image, require good time resolution only, which suggests minimizing only the time duration of the wavelet function. The results of minimization of the time duration of wavelets is described. As in Morris, Akunuri, and Xie (1995), the time duration of a wavelet function is expressed as a function of the wavelet-defining filter of length N. For a given N, the minimization is done over all possible orthonormal wavelets. The minimum duration wavelets (MDW) designed will be best suited for applications requiring good time resolution. Some examples along with comparisons with other wavelets are presented.