Linear‐phase biorthogonal wavelet function with arbitrary regularity

Abstract

AbstractThis paper proposes a method of derivation for the linear‐phase biorthogonal wavelet functions with an arbitrary regularity, based on the finite impulse response (FIR) half‐band digital filter. Within the range of the orthogonal wavelet functions at present, the Haar function is the only one that satisfies the linear‐phase property. In the image processing and other applications, the linear‐phase property is more important than the orthogonality.From such a viewpoint, the biorthogonal wavelet functions are proposed, for which the orthogonality condition can be relaxed and the linear‐phase property can be emphasized. In its derivation, however, mathematical sophistication is involved and the range of the derived function is considerably limited. With the development of the wavelet transform in recent years, it has become more important to select the base function flexibly according to the purpose of the processing and it is desired to establish a derivation method for the more general biorthogonal wavelet function with a higher degree of freedom.This paper presents a derivation method for the more general biorthogonal wavelet function with an arbitrary regularity. the method is based on the half‐band digital filter, and the flat response is added to the filter composing the wavelet function. Then the regularity condition for the function is considered, and the amplitude square‐error is used as the evaluation function. Finally, several design examples are shown for the linear‐phase wavelet function derived by the proposed method.