Wavelets - Caltech Multi-Res Modeling Group

We can reconstruct the signal as:
Z
da dt
f (t) =c WF ( ;a) ha; (t)
a2 INTRODUCTION 13
where c is a constant depending on h(t). The reconstruction looks like a sum of coefficients of orthogonal
bases, but the ha; (t) are in fact highly redundant, since they are defined for every point in the a; space.
Nevertheless the formula above is correct if R h 2 (t) dt is finite and R h(t) dt = 0 (well, almost).
7 From Continuous to Discrete and Back
Since there is a lot of redundancy in the continuous application of the basic wavelet, a natural question
if whether we can discretize a and in such a way that we obtain a true orthonormal basis. Following
Daubechies [49] one can notice that if we consider two scales a0