Minimal factorization of lapped unimodular transforms
نویسندگان
چکیده
The Lapped Orthogonal Transform (LOT) [ I ] is a popular transform and has found many applications in signal processing. Its extension, BiOrthogonal Lapped Transform (BOLT), has been investigated in detail in [2]. In this paper, we will study Lapped Unimodular Transform (LUT). All of these three transforms are first-order matrices with FIR inverses. We will show that like LOT and BOLT, all LUTs can be factorized into degree-one unimodular matrices. The factorization is both minimal and complete. We will also show that all first-order systems with FIR inverses can be minimally factorized as a cascade of degree-one LOT, BOLT, and unimodular building blocks. However unlike LOT and BOLT, unimodular filter banks of any order (which include LUTs as a special case) can never have linear phase.
منابع مشابه
Lapped unimodular transform and its factorization
Two types of lapped transforms have been studied in detail in the literature, namely, the lapped orthogonal transform (LOT) and its extension, the biorthogonal lapped transform (BOLT). In this paper, we will study the lapped unimodular transform (LUT). All three transforms are first-order matrices with finite impulse response (FIR) inverses. We will show that like LOT and BOLT, all LUTs can be ...
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