Orthogonal Filter Banks
D. Sundararajan · 2015
The basis functions of the discrete wavelet transform (DWT) are a linear combination of sinusoids. In this chapter, the design of bandpass filters is illustrated by deriving the impulse response of some commonly used filters. The design of filters for DWT is different from that of the conventional filter design methods. In the chapter, the design of filters for orthogonal filter banks is presented. The design is illustrated for the commonly used filters: Haar filter, Daubechies filter of length four (D4), and Coiflet filter of length six (C6). Orthogonality of two real discrete sequences is the property of having the sum of products being one or zero under specified conditions. The chapter considers the orthogonality condition in the frequency domain. In DWT applications, it is important to select the appropriate type of filter, its length, and the number of levels of decomposition that best suits the specific application.