Multirate systems and filter banks
Multirate systems and filter banks
The Complexity of the Quaternion Product
The Complexity of the Quaternion Product
The GenLOT: generalized linear-phase lapped orthogonal transform
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
IEEE Transactions on Signal Processing
Quaternion multiplier inspired by the lifting implementation of plane rotations
IEEE Transactions on Circuits and Systems Part I: Regular Papers
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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.