On families of 2N-dimensional hypercomplex algebras suitable for digital signal processing
نویسنده
چکیده
A survey of hypercomplex algebras suitable for DSP is presented. Generally applicable properties are obtained, including a paraunitarity condition for hypercomplex lossless systems. Algebras of dimension n = 2 , N ∈ Z, are classified by generation methods, constituting families. Two algebra families, which hold commutative and associative properties for arbitrary N, are examined in more detail: The 2 -dimensional hyperbolic numbers and tessarines. Since these non-division algebras possess zero divisors, orthogonal decomposition of hypercomplex numbers is investigated in general.
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تاریخ انتشار 2006