Code covered by the BSD License
 Bspline toolbox
 bspline0( x )Bspline function of 0th order
 bspline1( x )Bspline function of 1st order
 bspline2( x )Bspline function of 2nd order
 bspline3( x )Bspline function of 3rd order
 bspline3dtrans( x )Direct transform specialised for 3rd order bspline
 bspline4( x )Bspline function of 4th order
 bsplineNdtrans( x, N, bou...bsplineNdtrans  polynomial Bspline direct transform
 bsplineNidtrans( x, N, bo...bsplineNdtrans  polynomial Bspline direct transform
 bsplineNkernel(k,n,m)centered Bspline kernel of order n, expansion factor m
 calcBsplineRoot( N )Calculate the roots for the direct filter coefs (z polynomial) of an Nth
 calcBsplineRootTable( )
 evalBsplineN1dim( c, n, x...Evaluate Bspline across 1st nonsingleton dimension
 evalBsplineNpoint( c, n, ...Evaluate centered spline at single point
 evalBsplineNpoints( c, n,...Evaluate polynomial Bspline at an array of points
 filterAPfwd1ord( x, zi )filterAPfwd1ord  forward direction 1st order allpole filter
 filterAPrev1ord( x, zi )filterAPrev1ord  reverse direction 1st order allpole filter
 filterAPsym2ord( x, zi, b...filterAPsym2ord  symmetrical 2. order allpole filter
 filterFIR( b, x, boundary...filterFIR  FIR filter with functional boundary conditions
 filterFIRmirror(b,x)
 forward1ordAp_simple( x, ...forward direction 1st order allpole filter
 idtrans_FIR_coefs(N)Use a precalculated table for loworder splines
 mirrorbound_1(x, bidx, bdms)Calculate mirrored data off boundary of x, in dimension bdm
 mirrorbound_2(x, bidx, bdms)
 mirroridx(idx,M)
 mirroridx_hs(idx,M)
 mirrorpad(x, m)
 resample_spline3()Spline 3 resampler which supports the image processing toolbox interface
 reverse1ordAp_simple( cp,...reverse direction 1st order allpole filter
 symm2ordAp_simple( x, zi )symmetrical 2. order allpole filter
 testBsplineN
 testBsplineObject
 testFilters
 testMscale
 testPadding
 u2N_FIR_coefs(N)u2n_FIR_coefs  filter coefficients for Bspline scale relation
 y=bsplineGeneralN(x,n)Bspline function of order n
 y=bsplineN(x,n)Bspline function of order n
 Bspline
 MscaleBspline
 pyramid_example.m

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Bspline tools
by
Jan Tore Korneliussen
22 Mar 2010
(Updated
08 May 2011)
Basic toolbox for polynomial Bsplines on a uniform grid. OO overloading of common operators.

u2N_FIR_coefs(N) 
function [u2N, c] = u2N_FIR_coefs(N)
% u2n_FIR_coefs  filter coefficients for Bspline scale relation
%
% [u2N, c] = u2N_FIR_coefs(N) generates the FIR filter u2N which relates two
% scalings of the bspline basis:
%
% b_N_2 = c*conv(u2N, b_N)
%
% where b_N and b_N_2 are two discretized versions of the basic Bspline
% of order N, b_N_2 is dilated with a factor of two:
%
% b_N_2 = beta_N(k/2) for k = Inf, Inf
% b_N = beta_N(k) for k = Inf, Inf
%
% c is an additional scale factor.
u2N = zeros(1,N+2);
c = 2^(N);
for k = ((N+1)/2):((N+1)/2);
u2N(k+(N+1)/2+1) = nchoosek((N+1),k+(N+1)/2);
end


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