Databases Reference
In-Depth Information
13.8 Summary
In this chapter, we have described the concept of transform coding and provided some of the
details needed for the investigation of this compression scheme. The basic encoding scheme
worksasfollows:
Divide the source output into blocks. In the case of speech or audio data, they will be
one-dimensional blocks. In the case of images, they will be two-dimensional blocks. In
image coding, a typical block size is 8
×
8. In audio coding, the blocks are generally
overlapped by 50%.
Take the transform of this block.
In the case of one-dimensional data, this involves
premultiplying the
N
1 vector of source output samples by the transformmatrix. In the
case of image data, for the transforms we have looked at, this involves premultiplying the
N
×
×
N
block by the transform matrix and post-multiplying the result with the transpose
of the transform matrix. Fast algorithms exist for performing the transforms described
in this chapter (see [
201
]).
Quantize the coefficients. Various techniques exist for the quantization of these coeffi-
cients. We have described the approach used by JPEG. In Chapter 16 we describe the
quantization techniques used in various audio coding algorithms.
Encode the quantized value. The quantized value can be encoded using a fixed-length
code or any of the different variable-length codes described in earlier chapters. We have
described the approach taken by JPEG.
The decoding scheme is the inverse of the encoding scheme for image compression. For the
overlapped transform used in audio coding, the decoder adds the overlapped portions of the
inverse transform to cancel aliasing.
The basic approach can be modified depending on the particular characteristics of the
data. We have described some of the modifications used by various commercial algorithms
for transform coding of audio signals.
Further Reading
1.
For detailed information about the JPEG standard,
JPEG Still Image Data Compression
Standard
, by W.B. Pennebaker and J.L. Mitchell [
6
], is an invaluable reference. This
book also contains the entire text of the official draft JPEG recommendation, ISO DIS
10918-1 and ISO DIS 10918-2.
2.
For a detailed discussion of the MDCT and how it is used in audio coding, an excellent
source is
Introduction to Digital Audio Coding Standards
, by M. Bosi and R.E. Goldberg
[
200
].
3.
Chapter 11 in
Digital Coding of Waveforms
, by N.S. Jayant and P. Noll [
134
], provides
a more mathematical treatment of the subject of transform coding.
4.
A good source for information about transforms is
Fundamentals of Digital Image Proc-
essing
,byA.K.Jain[
202
]. Another one is
Digital Image Processing
, by R.C. Gonzales
