Translations:Appendix G: Exercises/48/en

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18. Discuss: Why is a zero-phase wavelet anticipatory? [Answer: It begins before time zero.] Phase curves depend on the location of the time reference point. Other mixed-phase wavelets also can be constructed from the same component dipoles. An important feature of a minimum-phase wavelet is that its energy arrives as soon as possible, consistent with its amplitude spectrum. Consider a set of possible filters with identical amplitude spectra. The minimum-phase filter is the one that delays the energy the least. Therefore, it also is called a minimum-delay filter. If the input to a minimum-phase filter is itself minimum phase, then the output also will be minimum phase. Much of the filtering performed during digital processing is of the minimum-phase type. A minimum-phase wavelet is sometimes said to be front-loaded because its energy is concentrated in the front end of the wavelet. Maximum-phase or maximum delay is the other extreme, because energy is concentrated in the back end of the wavelet. Mixed-phase is an intermediate case, with energy concentrated at intermediate positions of the wavelet.