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The packages supports discrete B-splines as defined by

B-Spline Signal Processing: Part I`Unser et al., IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 2

\[b^n_m(k) = \beta^n(k/m)\]

In the figure below we show two examples of such discrete B-splines, namely, $b^1_3$ and $b^3_2$

For oversampled discrete B-splines ($m>1$) there exist compact duals, i.e., signals, $g$, such that

\[\langle \delta_{lm} * b^n_m, \delta_{km} * g\rangle=\delta_{l-k},\quad \forall l,k\in \mathbb Z.\]

Their support is restricted to $k=-R,\dots,R$. Below you see some compact dual signals for the discrete B-splines above.

bn(n::Int, ::Type{T}=Float64)

Discrete B-spline signal of degree n and period mN.

Implements the signals of B-Spline Signal Processing: Part I
Unser et al., IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 2

bnm(n::Int, m::Int, [N::Int, ]::Type{T}=Float64)

Discrete B-spline signal of degree n and oversampling m. If 'N' is specified the signal is periodic with period Nm.

Implements the signals of B-Spline Signal Processing: Part I
Unser et al., IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 2

bsplinesignal(n::Int, [, m::Int] ::Type{T}=Float64)

Discrete B-spline signal of degree n and oversampling m.

Implements the signals of B-Spline Signal Processing: Part I
Unser et al., IEEE TRANSACTIONS ON SIGNAL PROCESSING, VOL. 41, NO. 2

b̃nm(n::Int, m::Int, N::Int, ::Type{T}=Float64)

Least squares dual of bnm:

$b̃nm(k)= \left[\left([bnm*bnm]_{↓m}\right)^{-1}\right]_{↑m}*bnm(k)$.

periodicbsplinesignal(n::Int, m::Int, N::Int, ::Type{T}=Float64)

Discrete B-spline signal of degree n, oversampling m and period mN.