Databases Reference
In-Depth Information
Decimate the output of the filters.
Encode the decimated output.
The decoding procedure is the inverse of the encoding procedure. When encoding images
the filtering and decimation operations have to be performed twice, once along the rows and
once along the columns. Care should be taken to avoid problems at edges, as described in
Section
14.12
.
Further Reading
1.
Handbook for Digital Signal Processing
, edited by S.K. Mitra and J.F. Kaiser, is an
excellent source of information about digital filters [
276
].
2.
Multirate Systems and Filter Banks
, by P.P. Vaidyanathan [
206
], provides detailed in-
formation on quadrature mirror filters, as well as the relationship between wavelets and
filter banks and much more.
3.
The topic of subband coding is also covered in
Digital Coding of Waveforms
,byN.S.
Jayant and P. Noll [
134
].
4.
The MPEG-1 audio coding algorithm is described in “ISO-MPEG-1 Audio: A Generic
Standard for Coding of High-Quality Digital Audio,” by K. Brandenburg and G. Stoll ,
in the October 1994 issue of the
Journal of the Audio Engineering Society
[
277
].
5.
A review of the rate distortion method of bit allocation is provided in “Rate Distortion
Methods for Image and Video Compression,” by A. Ortega and K. Ramachandran, in the
November 1998 issue of
IEEE Signal Processing Magazine
[
278
].
14.14 Projects and Problems
1.
A linear shift invariant system has the following properties:
If for a given input sequence
{
x
n
}
the output of the system is the sequence
{
y
n
}
,
then if we delay the input sequence by
k
units to obtain the sequence
{
x
n
−
k
}
,the
corresponding output will be the sequence
{
y
n
}
delayed by
k
units.
x
(
1
)
y
(
1
)
If the output corresponding to the sequence
{
}
is
{
}
, and the output cor-
n
n
x
(
2
)
y
(
2
)
{
}
{
}
responding to the sequence
is
, then the output corresponding to the
n
n
x
(
1
)
x
(
2
)
y
(
1
)
y
(
2
)
sequence
{
α
+
β
}
is
{
α
+
β
}
.
n
n
n
n
Use these two properties to show the convolution property given in Equation (
18
).
2.
Let's design a set of simple four-tap filters that satisfies the perfect reconstruction
condition.
