Biorthogonal Filter Banks
D. Sundararajan · 2015
This chapter discusses the biorthogonality conditions and presents the design of discrete wavelet transform (DWT) biorthogonal filters: 5/3 and 4/4 spline filters and the CDF 9/7 filter. It provides the solution to design two lowpass filters and derive the highpass filters from them. The design can proceed in the same way as that for the orthogonal filters, with the difference that the resulting set of equations must be solved for two filters. The chapter illustrates a two-channel filter bank with biorthogonal 5/3 and 4/4 spline filters. It provides Daubechies formulation to derive the 5/3 and 4/4 spline filters. The magnitude of the frequency responses of the 5/3, 4/4 and CDF 9/7 spline analysis filters are also shown. In DWT applications, it is important to select the appropriate filter type, its length, and the number of iterations that best suits the specific application.