Modulated, perfect reconstruction filterbanks with integer coefficients

Abstract

We present design methods for perfect reconstruction (PR) integer-modulated filterbanks, including biorthogonal (low-delay) filterbanks. Both the prototype filter and the modulation sequences are composed of integers, thus allowing efficient hardware implementations and fast computation. To derive such filterbanks, we first start with the PR conditions known for cosine modulation and extend them to more general, integer modulation schemes. For the design of biorthogonal PR integer prototypes, a lifting strategy is introduced. To find suitable integer modulation schemes, new algebraic methods are presented. We show solutions where the PR conditions on the prototype filters and the modulation matrices are entirely decoupled and where some simple coupling is introduced. Both even and odd numbers of channels are considered. Design examples are presented for both cases. -modulated filterbanks, including biorthogonal (low-delay) filterbanks. Both the prototype filter and the modulation sequences are composed of integers, thus allowing efficient hardware implementations and fast computation. To derive such filterbanks, we first start with the PR conditions known for cosine modulation and extend them to more general, integer modulation schemes. For the design of biorthogonal PR integer prototypes, a lifting strategy is introduced. To find suitable integer modulation schemes, new algebraic methods are presented. We show solutions where the PR conditions on the prototype filters and the modulation matrices are entirely decoupled and where some simple coupling is introduced. Both even and odd numbers of channels are considered. Design examples are presented for both cases. Disciplines Physical Sciences and Mathematics

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Performance analysis and prototype filter design for perfect-reconstruction cosine-modulated filter banks with fixed-point implementation

“…1. For the considered delay of taps, the modulation matrices in (5) and (6) can be expressed using the orthonormal DCT-4 matrix as [10], [13].…”

“…The difference to a realization of two polyphase filters using lifting, as described in [2], [10], is that we here realize four polyphase filters simultaneously, thus saving a factor of two in terms of computational complexity. Polyphase, butterfly, and modulation matrices were scaled such that none of them performs an unnecessary amplification of the input signal.…”

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