Databases Reference
In-Depth Information
Further Reading
1.
There are a number of excellent introductory topics on wavelets. One of the most ac-
cessible is
Introduction to Wavelets and Wavelet Transforms—A Primer
, by C.S. Burrus,
R.A. Gopinath, and H. Guo [
212
].
2.
Probably the best mathematical source on wavelets is the topic
Ten Lectures on Wavelets
,
by I. Daubechies [
279
].
3.
There are a number of tutorials on wavelets available on the Internet. The best source
for all matters related to wavelets (and more) on the Internet is “The Wavelet Digest”
(
<http://www.wavelet.org>
)
. This site includes pointers to many other interesting and
useful sites dealing with different applications of wavelets.
15.9 Projects and Problems
1.
In this problem we consider the boundary effects encountered when using the short-term
Fourier transform. Consider the signal
f
(
t
)
=
sin
(
2
t
)
(a)
Find the Fourier transform
F
(ω)
of
f
(
t
)
.
(b)
Find the STFT
F
1
(ω)
of
f
(
t
)
using a rectangular window
1
−
2
t
2
g
(
t
)
=
0 otherwise
2, 2].
(c)
Find the STFT
F
2
(ω)
for the interval [
−
of
f
(
t
)
using a window
1
(
2
t
+
cos
)
−
2
t
2
g
(
t
)
=
0
otherwise
|
(ω)
|
,
|
F
1
(ω)
|
|
F
2
(ω)
|
(d)
Plot
F
, and
. Comment on the effect of using different window
functions.
2.
For the function
1
+
(
)
sin
2
t
0
t
1
f
(
t
)
=
sin
(
2
t
)
otherwise
use the Haar wavelet to find and plot the coefficients
{
c
j
,
k
}
,
j
=
0
,
1
,
2
;
k
=
0
,...,
10.
