Framelet

Such symmetric quincunx tight framelets are associated with quincunx tight framelet filter banks #92;#123;a#59;b#95;1,b#95;2,b#95;3#92;#125; having increasing orders of vanishing moments and enjoying the additional double canonical properties: b#95;1(k#95;1,k#95;2)#61;(-1)#123;1#43;k#95;1#43;k#95;2#125;a(1-k#95;1,-k#95;2),b#95;3(k#95;1,k#95;2)#61;(-1)#123;1#43;k#95;1#43;k#95;2#125;b#95;2(1-k#95;1,-k#95;2). For a low-pass filter a which is not a quincunx orthonormal wavelet filter, we show that a quincunx tight framelet filter bank #92;#123;a#59;b#95;1,#92;ldots,b#95;L#92;#125; with b#95;1 taking the above canonical form must have L#92;ge 3 high-pass filters.