Complete Factorization of the 2m-Band Paraunitary Polyphase Matrix with Multiple Centers of Symmetry

2019 ◽  
Vol 39 (5) ◽  
pp. 2533-2549
Author(s):  
Guoqiu Wang ◽  
Yong Chen ◽  
Dingxun Yi
Keyword(s):  
Polyphase Matrix ◽  
Complete Factorization

Factorization in LCM Domains with Conjugation

1994 ◽  
Vol 37 (3) ◽  
pp. 289-293 ◽  
Author(s):  
Raymond A. Beauregard
Keyword(s):  
Integral Domain ◽  
Complete Factorization

AbstractAn atomic integral domain with conjugation has unique (in the sense of Theorem 6 below) factorization of atomic factors if it is an LCM domain. If the LCM hypothesis is dropped not even the number of atomic factors in a complete factorization of an element need be unique.

The Complete Factorization of 2 132 + 1

1960 ◽  
Vol 14 (69) ◽  
pp. 73
Author(s):  
K. R. Isemanger
Keyword(s):  
Complete Factorization

scholarly journals Symmetry Feature and Construction for the 3-Band Tight Framelets with Prescribed Properties

2012 ◽  
Vol 2012 ◽  
pp. 1-20
Author(s):  
Jianjun Sun ◽  
Bin Huang ◽  
Xiaodong Chen ◽  
Lihong Cui
Keyword(s):  
Wavelet Frames ◽  
Symmetric Extension ◽  
The Matrix ◽  
Polyphase Matrix ◽  
Necessary Constraints ◽  
Sobolev Exponent

A construction approach for the 3-band tight wavelet frames by factorization of paraunitary matrix is developed. Several necessary constraints on the filter lengths and symmetric features of wavelet frames are investigated starting at the constructed paraunitary matrix. The matrix is a symmetric extension of the polyphase matrix corresponding to 3-band tight wavelet frames. Further, the parameterizations of 3-band tight wavelet frames with3N+1filter lengths are established. Examples of framelets with symmetry/antisymmetry and Sobolev exponent are computed by appropriately choosing the parameters in the scheme.

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