Bi-orthogonal rational discrete wavelet transform with multiple regularity orders and application experiments

• A method is presented for designing two-channel FIR rational FBs with regularity and flexible Q factor.
• Signals being benefited are of oscillatory nature such as speech signal.
• Dictionary can be constructed from the design RADWT and dyadic wavelet in an l1 problem.
• The proposed biorthogonal RADWT can be used effectively with dyadic wavelet for signal separation.

This paper proposes an approach for designing a general two-band, FIR, critically sampled, rational rate filter bank (RFB) with perfect reconstruction (PR) and regularity properties. Designs obtained from this approach, when iterated, lead to rational discrete wavelet transforms (RADWTs) with adjustable dilation factor. The RFB design is based on solving a non-convex constrained optimization problem in which the non-linear constraints arise from the perfect reconstruction conditions. An iterative algorithm is used to solve the optimization problem through solving a simplified convex quadratic problem with linear constraints at each iteration step. Some examples are provided to demonstrate the use of bi-orthogonal RADWTs in applications such as signal separation which benefit from decompositions with suitably chosen dilation factors.