Cryptography Reference
In-Depth Information
Meyer psi
H
t
L
of order 2
0.5
t
-4
-2
2
4
-0.5
-1
Figure 14.14: The Meyer
ψ
function.
14.8 Wavelets
Many of the algorithms use sines and cosines as the basis for con-
structing models of data, but there is no reason why the process
should be limited to them alone. In recent years, researchers be-
gan devoting new energy to exploring how strange and different
functions can make better models of data- a field the researchers
call
wavelets
. Figure 14.14 shows one popular wavelet function, the
Meyer
ψ
function.
Some of the
steganography detection
algorithms examine the
statistics of wavelet
decompositions. See
Section 17.6.1.
Wavelet transforms construct models of data in much the same
way Fourier transforms or Cosine transforms do— they compute co-
efficients that measure how much a particular function behaves like
the underlying data. That is, the computation finds the correlation.
Most wavelet analysis, however, adds an additional parameter to the
mix by changing both the frequency of the function and the loca-
tion or window where the function is non-zero. Fourier transforms,
for instance, use sines and cosines that are defined from
.
Wavelet transforms restrict the influence of each function by sending
the function to zero outside a particular window from
−∞
to
+
∞
a
to
b
.
