Databases Reference
In-Depth Information
1.5
1
0.5
f
(
t
/0.5)
0
−0.5
−1
−
1.5
−2
−
1.5
−1
−
0.5
0
0.5
1
1.5
2
t
The function f (
0.5
).
F I GU R E 15 . 5
1.5
1
0.5
f
((
t
-1)/0.5)
0
−0.5
−1
−
1.5
−2
−1.5
−1
−0.5
0
0.5
1
1.5
2
t
F I GU R E 15 . 6
A scaled and translated function.
If this family of functions satisfies certain properties we can use them to represent signals of
interest in a manner similar to the Fourier basis functions. Unlike the Fourier basis functions,
because these functions are localized in time and frequency we can use themwithout giving up
all the temporal information contained in the original function. Because of their limited spatial
extent these functions were originally called
ondelettes
, which is French for small waves, or
wavelets
.
