View source for Framelet

==English==

===Etymology===
From {{suffix|en|frame|let}}.

===Noun===
{{en-noun}}

# {{lb|en|maths}} A [[wavelet]] [[frame]].
#* {{quote-journal|en|author=Bin Han; Qingtang Jiang; Zuowei Shen; Xiaosheng Zhuang|title=Symmetric Canonical Quincunx Tight Framelets with High Vanishing Moments and Smoothness [arXiv:1507.07492v1]|url=http://arxiv.org/abs/1507.07492|journal=w:arXiv|date=27 July 2015|passage=Such symmetric quincunx tight '''framelets''' are associated with quincunx tight '''framelet''' filter banks <math>\{a;b_1,b_2,b_3\}</math> having increasing orders of vanishing moments and enjoying the additional double canonical properties: <math>b_1(k_1,k_2)=(-1)^{1+k_1+k_2} a(1-k_1,-k_2), b_3(k_1,k_2)=(-1)^{1+k_1+k_2} b_2(1-k_1,-k_2).</math> For a low-pass filter <math>a</math> which is not a quincunx orthonormal wavelet filter, we show that a quincunx tight '''framelet''' filter bank <math>\{a;b_1,\ldots,b_L\}</math> with <math>b_1</math> taking the above canonical form must have <math>L\ge 3</math> high-pass filters.}}