Translations:Symmetric wavelets/12/en

No wavelet exists that can be restricted to a finite time interval with a spectrum simultaneously restricted to a finite frequency band. However, various tapered wavelets are restricted to a finite time interval and do have spectra with much lower side lobes than is the case for the spectrum of the rectangular wavelet. A tapered wavelet must rise in amplitude less sharply than the rectangular wavelet does so its spectrum will contain less high-frequency energy. In fact, the occurrence of sharp discontinuities in a wavelet’s shape or derivatives should be avoided whenever possible, to achieve reduced spectral energy in spectral side-lobe regions.