By making a discrete finite time signal periodic, it is shown that
nonorthogonal B-spline wavelets can be used in a discrete wavelet
transform with exact decomposition and reconstruction. A non-recursive
algorithm using only Finite Impulse Response filters (FIR) with
complexity O(N^2) is presented. The complexity is reduced
to O(N log(N)) by using Fast Fourier Transforms (FFT).
A faster algorithm is obtained by using recursive filters in the
decomposition or reconstruction of the signal. The recursive algorithm
has complexity O(N), and the same accuracy as the others.
By allowing non-symmetric wavelets, an exact orthogonal reconstruction
algorithm is shown, which also has complexity O(N).