TITLE: What is a cardinal basis spline?
QUESTION [7 upvotes]: Wikipedia says: 

the normalized cardinal B-splines tend to the Gaussian function

and writes them as "Bk".  Meanwhile, cnx.org Signal Reconstruction says: 

The basis splines Bn are shown ... as the order increases, the functions approach the Gaussian function, which is exactly B∞.


but then says

as the order increases, the cardinal basis splines approximate the sinc function, which is exactly η∞.


Likewise, Signal Reconstruction with Cardinal Splines uses similar notation of ηn for "cardinal spline".
So which is it?  Does a "cardinal basis spline" approximate a Gaussian or a sinc?  "B-spline" and "basis spline" are the same thing, right?  Is there any relationship to this cardinal spline?

REPLY [3 votes]: Roughly speaking ...
If you fix certain quantities (degree, knots, orders of continuity) then the set of all splines forms a vector space, which, of course, has several different bases.
Two common bases are the cardinal splines, and the b-splines.
It's true that "b-spline" is an abbreviation of "basis spline", but the vector space of splines has other bases, besides the b-splines. Confusing, I guess.
I wasn't aware of the limits as degree goes to infinity, but the statements sound plausible. Assuming you use the right knot sequences, I can see how the b-spline basis functions might tend to the Gaussian function, and the cardinal basis functions might tend to the sinc function.