In recent years, the theory of filter banks has been developed rapidly since they are widely used in many scientific areas such as signal and image processing, data mining, data feature extraction, and compressive sensing. In the theory, the perfect reconstruction filter banks (PRFBs) play an important role [7,8,20–23].
A PRFB consists of two sub-filter banks: an analysis filter bank, which is used to decompose signals into different bands, and a synthesis filter bank, which is used to compose a signal from its different band