Wavelets - Caltech Multi-Res Modeling Group

Heisenberg inequality that bounds their product:
Δt Δf
1
4
INTRODUCTION 11
The lower bound is achieved by the Gaussian [87]. The other aspect of this problem is that once the window
is chosen, the resolution limit is the same over all times and frequencies. This means that there is no
adaptability of the analysis, and if we want good time resolution of the short bursts, we have to sacrifice
good frequency description of the long smooth sections.
To illustrate with a piece-wise constant transform, we can use the Walsh transform again, and use a box as
the window. The box is defined as:
(
1
w(t) =
0
if , 2 t