Graphics Reference
In-Depth Information
•
()( )
=<
Ú
()
()
WT f i j
,
w
,
f
>=
f x
y
x dx
.
ji
,
ji
,
-•
Theorem 21.9.2 implies that if the discrete Haar wavelet transform (computing
the coefficients of a function with respect to the Haar basis functions) is known, then
one can reconstruct the function.
Finally, with regard to higher dimensions, in dimension two we can take the
“tensor product” of one-dimensional wavelets to get the obvious extension. Wavelets
are a very active field of research currently with many applications in a great variety
of fields, in particular, computer graphics.
21.10
E
XERCISES
Section 21.5
21.5.1
Verify that the following Fourier series are correct on (-p,p).
-
()
-
n
1
•
Â
1
sin
nx
(a)
x
=
2
n
n
=
1
n
2
•
Â
-
()
p
1
cos
nx
2
(b)
x
=+
4
2
3
n
n
=
1
n
•
Â
-
()
1
2
1
n x
sin
(c)
xx
cos
=-
sin
x
+
2
2
n
-
1
n
=
2
