PEBFUN Sampled, periodized EB-spline
Usage: g=pebfun(L,w)
g=pebfun(L,w,width)
[g,nlen]=pebfun(...)
Input parameters:
L : Window length.
w : Vector of weights of g*
width : integer stretching factor, the support of g is width*length(w)
Output parameters:
g : The periodized EB-spline.
nlen : Number of non-zero elements in out.
PEBFUN(L,w) computes samples of a periodized EB-spline with weights
w for a system of length L.
PEBFUN(L,w,width) additionally stretches the function by a factor of
width.
[g,nlen]=ptpfundual(...) as g might have a compact support,
nlen contains a number of non-zero elements in g. This is the case
when g is symmetric. If g is not symmetric, nlen is extended
to twice the length of the longer tail.
If nlen = L, g has a 'full' support meaning it is a periodization
of a EB spline function.
If nlen < L, additional zeros can be removed by calling
g=middlepad(g,nlen).
References:
K. Groechenig and J. Stoeckler. Gabor frames and totally positive
functions. Duke Math. J., 162(6):1003--1031, 2013.
S. Bannert, K. Groechenig, and J. Stoeckler. Discretized Gabor frames of
totally positive functions. Information Theory, IEEE Transactions on,
60(1):159--169, 2014.
T. Kloos and J. Stockler. Full length article: Zak transforms and gabor
frames of totally positive functions and exponential b-splines. J.
Approx. Theory, 184:209--237, Aug. 2014. [1]http ]
T. Kloos. Gabor frames total-positiver funktionen endlicher ordnung.
Master's thesis, University of Dortmund, Dortmund, Germany, 2012.
T. Kloos, J. Stockler, and K. Groechenig. Implementation of discretized
gabor frames and their duals. IEEE Transactions on Information Theory,
62(5):2759--2771, May 2016.
References
1. http://dx.doi.org/10.1016/j.jat.2014.05.010
Url: http://ltfat.github.io/doc/fourier/pebfun.html
See also: dgt, pebfundual, gabdualnorm, normalize.
Package: ltfat