Time-Frequency Localization Optimized

Abstract—The time-frequency product of any function in 퐿2 (ℝ) is bounded by the uncertainty principle. This paper presents a method to design linear phase biorthogonal wavelets with the time-frequency localization as the optimality criterion, improving on the previous designs on the same theme. The design philosophy is to optimize the time-frequency product of the wavelet, after fixing the number of vanishing moments of the analysis and synthesis lowpass filters of the corresponding filter bank. The regularity of the discrete filters has also been evaluated. Index Terms—biorthogonal filter banks, linear phase, wavelets, time-frequency localization. I