first.last(LengthH, DataLength, bc="periodic")"periodic" or "symmetric".If bc="periodic" then the pyramid is a true power of 2 pyramid, that is it starts with a power of 2, and the next level is half of the previous. If bc="symmetric" then the pyramid is nearly exactly a power of 2, but not quite, see the Details section for why this is so.
bc="periodic" this is indeed what happens.
However, if bc="symmetric" you actually need more than 1024 (as
the wavelets extend over the edges). The first/last database keeps track
of where all these "extras" appear and also where they are located in
the packed vectors C and D of pyramidal coefficients within wavelet
structures.For example, given a first.last.c row of
-2 3 20
The actual coefficients would be
$c_{-2}, c_{-1}, c_{0}, c_{1}, c_{2}, c_{3}$.
In other words, there are 6 coefficients, starting at -2 and ending at 3, and the first of these ($c_{-2}{c_{-2}}) appears at an offset of 20 from the beginning of the \code{. $ C} component vector of the wavelet structure.
You can `do' first.last in your head for periodic boundary handling,
but for more general boundary treatments (e.g. symmetric) \code{first.last}
is indispensable.$
Daubechies, I. (1988).
Orthonormal bases of compactly supported wavelets;
Communications on Pure and Applied Mathematics, 41, 909-996.
wr, accessC, accessD,
filter.select, threshold, wd,
imwd, imwr.
first.last(length(filter.select(2)), 64)