کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
4600028 1336831 2012 30 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Matrix splitting with symmetry and dyadic framelet filter banks over algebraic number fields
چکیده انگلیسی

Algebraic number fields are of particular interest and play an important role in both mathematics and engineering since an algebraic number field can be viewed as a finite dimensional linear space over the rational number field Q. Algorithms using algebraic number fields can be efficiently implemented involving only integer arithmetics. In this paper, we properly formulate the matrix splitting problem over any general subfield of it C, including an algebraic number field as a special case, and provide a simple necessary and sufficient condition for a 2×2 matrix of Laurent polynomials with symmetry to be able to be factorized by a 2×2 matrix of Laurent polynomials with certain symmetry structure. We propose an effective algorithm on how to obtain the factorization matrix step by step. As an application, we obtain a satisfactory algorithm for constructing dyadic framelet filter banks with the perfect reconstruction property and with symmetry over algebraic number fields. Several examples are provided to illustrate the algorithms proposed in this paper.

ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Linear Algebra and its Applications - Volume 437, Issue 10, 15 November 2012, Pages 2650-2679