Design and factorization of FIR paraunitary filter banks given several analysis filters

This correspondence discusses the design and factorization of FIR paraunitary filter banks where several analysis filters are given. A lattice factorization-based algorithm is presented that provides complete and minimal characterization for nonlinear-phase and balanced linear-phase systems. As a result, the design problem can be formulated as an unconstrained optimization of the lattice coefficients, whereas paraunitariness and linear-phase properties are structurally guaranteed. The second presented algorithm formulates the design problem in quadratic form that provides better control on the frequency responses of the embedding solution. An unitary scaling filter design algorithm is also presented that can be paired with the paraunitary embedding solution to design an orthonormal wavelet basis with high regularity. A design example is presented.