Abstract
A novel approach to the design and implementation of four-channel paraunitary filter banks is presented. It utilizes hypercomplex number theory, which has not yet been employed in these areas. Namely, quaternion multipliers are presented as alternative paraunitary building blocks, which can be regarded as generalizations of Givens (planar) rotations. The corresponding quaternionic lattice structures maintain losslessness regardless of coefficient quantization and can be viewed as extensions of the classic two-band lattice developed by Vaidyanathan and Hoang. Moreover, the proposed approach enables a straightforward expression of the one-regularity conditions. They are stated in terms of the lattice coefficients, and thus can be easily satisfied even in finite-precision arithmetic.
Highlights
Paraunitary filter banks (PUFBs) can be considered the most important among multirate systems [1]
It is more convenient to work with the analysis polyphase transfer matrix E(z), which is paraunitary if EH (z−1)E(z) = cIM, where c is a nonzero constant and M denotes the number of channels [2]
We propose a novel approach to the design and implementation of four-band PUFBs
Summary
Paraunitary filter banks (PUFBs) can be considered the most important among multirate systems [1]. The only exception is the two-band lattice structure reported in [7] These facts are not widely known because the effects of coefficient quantization in PUFBs were studied only in [8]. This is undoubtedly a consequence of the growing popularity of lifting factorizations, which guarantee perfect reconstruction under finite precision [9, 10]. They lead to biorthogonal systems with a complicated relation between the fullband and subband signal energies.
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