Quaternionic formulation of the first regularity for four-band paraunitary filter banks

This paper investigates the first regularity of the three main subclasses of four-band paraunitary filter banks (PUFBs): general, linear phase and those with pairwise-mirror-image (PMI) properties. It is considered from the perspective of quaternionic lattice structures known to maintain their orthogonality regardless of coefficient quantization. This approach turns out to be very useful anew, as the first regularity can be very straightforwardly expressed in terms of quaternionic lattice coefficients. Moreover, the property can be easily preserved in finite precision implementations, what is demonstrated by appropriate design examples