<s>
Wavelet	B-Algorithm
packet	I-Algorithm
bases	O
are	O
designed	O
by	O
dividing	O
the	O
frequency	O
axis	O
in	O
intervals	O
of	O
varying	O
sizes	O
.	O
</s>
<s>
Theorem	O
1	O
.	O
constructs	O
a	O
block	O
orthogonal	B-Algorithm
basis	I-Algorithm
of	O
from	O
a	O
single	O
orthonormal	O
basis	O
of	O
.	O
</s>
<s>
It	O
is	O
centered	O
at	O
and	O
has	O
a	O
slow	O
asymptotic	O
decay	O
proportional	O
to	O
Because	O
of	O
this	O
poor	O
frequency	O
localization	O
,	O
even	O
though	O
a	O
signal	O
is	O
smooth	O
,	O
its	O
decomposition	O
in	O
a	O
block	O
Fourier	O
basis	O
may	O
include	O
large	O
high-frequency	B-Algorithm
coefficients	O
.	O
</s>
<s>
Suppose	O
that	O
is	O
an	O
orthogonal	B-Algorithm
basis	I-Algorithm
of	O
for	O
any	O
.	O
</s>
<s>
As	O
in	O
the	O
continuous	O
case	O
,	O
the	O
decomposition	O
of	O
smooth	O
signals	O
may	O
produce	O
large-amplitude	O
,	O
high-frequency	B-Algorithm
coefficients	O
because	O
of	O
border	O
effects	O
.	O
</s>
