Translations:Dictionary:Phase characteristics/2/en

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Any wavelet may be represented as the convolution of doublets and a wavelet is minimum phase if all of its doublet factors are minimum phase. For example, the z-transform of a wavelet might be (6+zz2), which can be expressed as (3–z)(2+z), each of which is minimum phase; hence the wavelet is minimum phase. Minimum phase is sometimes expressed as having all roots outside the unit circle in the z-plane, or as having no zeros in the right half of the Laplace transform S-plane. A maximum-phase or maximum-delay doublet [a,b] has |a|<|b|. Maximum-phase wavelets have all their roots inside the unit circle in the z-plane. For a linear-phase wavelet, the phase-frequency plot is linear. If its intercept is nπ (where n is any integer), such a wavelet is symmetrical.