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The Stein Wavelet
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From  Meyer's
Wavelets - Algorithms & Applications
SIAM, 1993, Page 20
;[s]
3:0,0;14,1;50,2;71,-1;
3:1,16,12,Times,1,18,0,0,0;1,16,12,Times,2,18,0,0,0;1,16,12,Times,1,18,0,0,0;
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Jack K. Cohen
Colorado School of Mines, 1993
jkc@keller.mines.colorado.edu 
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<<Meyer.m
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The insight is that we can adapt the taper needed for the construction of the Littlewood-Paley-Stein mother wavelet from that used in the construction of the Meyer wavelet by stretching the latter from the interval [0, 1] to the intervals needed for the Littlewood-Paley-Stein mother wavelet and then ... taking a square root !
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Review of the Meyer Taper
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?NuTaper
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NuTaper[n, x] -- NuTaper returns a function of x that
   ascends from 0 to 1 over the interval [0, 1] with
   n^th degree smoothness at the endpoints.  The degree
   of the polynomial is 2n -1.
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NuTaper[1, x]
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x
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x
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NuTaper[2, x]
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(3 - 2*x)*x^2
;[o]
           2
(3 - 2 x) x
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Module for the Transform of the Stein Mother Wavelet
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Larger n gives a smoother taper.
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PsiHat[xi_, alpha_, n_] :=
Module[
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	Which[
		(* if *) 1 + alpha <= xi <= 2 - 2 alpha,
			(* then *) 1,
		(* elseif *) 1 - alpha <= xi < 1 + alpha,
			(* then *) taper[(xi - 1 + alpha)/(2 alpha)],
		(* elseif *) 2 - 2alpha < xi <= 2 + 2alpha,
			(* then *) taper[(2alpha + 2 - xi)/(4 alpha)],
		(* else *) True,
			(* then *) 0
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2^(-1/2)
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   1
-------
Sqrt[2]
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