Special paraunitary matrices, Cayley transform, and multidimensional orthogonal filter banks

Area of Science:

• Signal Processing
• Linear Algebra
• Multidimensional Systems

Background:

• Orthogonal filter banks are crucial in signal processing and are represented by paraunitary matrices in the polyphase domain.
• Designing these filter banks often involves solving complex nonlinear equations.

Purpose of the Study:

• To simplify the characterization and design of multidimensional (MD) orthogonal filter banks.
• To introduce a novel approach using special paraunitary matrices and the Cayley transform.

Main Methods:

• Characterizing paraunitary matrices via special paraunitary matrices (unit determinant) and phase factors.
• Utilizing the Cayley transform to convert nonlinear constraints into linear constraints.
• Developing a simplified design procedure for MD orthogonal filter banks.

Main Results:

• Every paraunitary matrix can be represented by a special paraunitary matrix and a phase factor.
• Special paraunitary matrices are fully characterized in the Cayley domain, simplifying design constraints.
• The proposed method significantly streamlines the design process for MD orthogonal filter banks.

Conclusions:

• The use of special paraunitary matrices and the Cayley transform offers a complete and simplified method for designing MD orthogonal filter banks.
• This approach reduces the complexity of the design problem by transforming nonlinear equations into linear ones.