g=pebfun(L,w) g=pebfun(L,w,width) [g,nlen]=pebfun(...)
| L | Window length. |
| w | Vector of weights of g |
| width | integer stretching factor, the support of g is width*length(w) |
| 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).
K. Gröchenig and J. Stöckler. Gabor frames and totally positive functions. Duke Math. J., 162(6):1003--1031, 2013.
S. Bannert, K. Gröchenig, and J. Stöckler. 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. [ DOI | http ]
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T. Kloos, J. Stockler, and K. Gröchenig. Implementation of discretized gabor frames and their duals. IEEE Transactions on Information Theory, 62(5):2759--2771, May 2016. [ DOI ]