Subband- and Wavelet-Based Coding - Digital Signal Processing: Fundamentals and Applications - page 621

CHAPTER

13

Subband- and Wavelet-Based
Coding

CHAPTER OUTLINE

13.1 Subband Coding Basics .............................................................................................................. 621
13.2 Subband Decomposition and Two-Channel Perfect Reconstruction Quadrature Mirror Filter Bank..... 626
13.3 Subband Coding of Signals ......................................................................................................... 635
13.4 Wavelet Basics and Families of Wavelets .................................................................................... 638
13.5 Multiresolution Equations ........................................................................................................... 650
13.6 Discrete Wavelet Transform ........................................................................................................ 655
13.7 Wavelet Transform Coding of Signals........................................................................................... 664
13.8 MATLAB Programs ...................................................................................................................... 668
13.9 Summary ................................................................................................................................... 672

OBJECTIVES
This chapter is a continuation of Chapter 12 and further studies basic principles of multirate digital signal
processing, specifically for subband and wavelet transform coding. First, the chapter explains digital filter
bank theory and develops subband coding techniques for compressing various signals, including speech
and seismic data. Then the chapter focuses on wavelet basics with applications of waveform coding and
signal denoising.

13.1 SUBBAND CODING BASICS
In many applications such as speech and audio analysis, synthesis, and compression, digital filter
banks are often used. The filter bank system consists of two stages. The first stage, called the
analysis stage, is in the form of filter bank decomposition, in which the signal is filtered into
subbands along with a sampling rate decimation; the second stage interpolates the decimated sub-
band signals to reconstruct the original signal. For the purpose of data compression, spectral
information from each subband channel can be used to quantize the subband signal efficiently to
achieve efficient coding.
Figure 13.1 illustrates the basic framework for a four-channel filter bank analyzer and synthe-
sizer. At the analysis stage, the input signal xðnÞ at the original sampling rate f s is divided via the
analysis filter bank into four channels, x 0 ðmÞ , x 1 ðmÞ , x 2 ðmÞ ,and x 3 ðmÞ , each at the decimated
sampling rate f s =M ,where M ¼ 4. For the synthesizer, these fo u r deci m ated s ignals are i nterpolated
via a synthesis filter bank. The outputs from all four channels ( x 0 ðnÞ , x 1 ðnÞ , x 2 ðnÞ ,and x 3 ðnÞ )ofthe