Subband Coding
Jennie Abraham
07/23/2009
Overview
Previously, different compression
schemes were looked into –
(i)Vector Quantization Scheme
(ii)Differential Encoding Scheme
(iii)Scalar Quantization Scheme
- Most efficient when the data exhibit
certain characteristics
Overview – cont’d
Source data characteristics Unfortunately, most source outputs
exhibit a combination of
characteristics.
 difficult to select a compression
scheme exactly suited to the source
output.
Overview - cont’d
Decomposing the source output into
constituent parts using some method.
Each constituent part is encoded using
one or more of the methods described
previously.
 enables the use of these compression
schemes more effectively.
Example 14.2.1
Yn
Compression
Scheme 1
Yn
Xn
Xn
Compression
Zn
Scheme 2
Zn
Example 14.2.1 – Cont’d
Xn = 10 14 10 12 14 8 14 12 10 8 10 12
Yn =
Xn = Yn + Zn
Zn =
Introduction to Subband Coding
The source output can be decomposed
into its constituent parts using digital
filters.
Each of these constituent parts will be
different bands of frequencies which
make up the source.
Subband Coding
A compression approach where digital
filters are used to separate the source
output into different bands of
frequencies.
Each part then can be encoded
separately.
Filters
A filter is system that isolates certain
frequencies.
(i)
(ii)
(iii)
Low Pass Filters
High Pass Filters
Band Pass Filters
Filters – Cont’d
Filter Characteristics

Magnitude Transfer Function : the
ratio of the magnitude of the input and
output of the filter as a function of
frequency.

fo = Cutoff Frequency.
Digital Filters
Sampling and Nyquist rule :
If fo is the highest frequency of the signal then the
sampling rate > 2fo per second can accurately
represent the continuous signal in digital form.
Extension of Nyquist rule:
For signal with frequency components between
frequencies f1and f2 then,
sampling rate = 2(f2 — f1) per second.
Violation of Nyquist rule:
Distortion due to aliasing.
Digital Filtering
The general form of the input-output
relationships of the filter is given by
where,
{Xn}= input, {Yn}=output of the filter,
Values {ai} and {bi} = filter coefficients,
N is called the taps in the filter.
 FIR Filter
 IIR Filter
Example 14.3.1
Filter Coefficients ao = 1.25, a1= 0.5 and the
input sequence {Xn} is given by –
then the output {Yn} is given by
Example 14.3.2
Consider a filter with ao = 1 and b1 = 2.
The input sequence is a 1 followed by 0s.
Then the output is
Filters in literature
Design and analysis of digital filters is
detailed in Sections 14.5-14.8 of the
textbook.
A useful approach is to make use of
the available literature to select the
necessary filters rather than design
them.
Filters used in Subband Coding
Couple of examples of –
Quadrature Mirror Filters (QMF),
Johnston Filter
Smith-Barnwell Filters
Daubechies Filters
….and so on
8-tap Johnston Low-Pass Filter
8-tap Johnston Low-Pass Filter
LP
HP
Filter Banks
Subband coding uses filter banks.
Filter banks are essentially a cascade of
stages, where each stage consists of a
low-pass filter and a high-pass filter.
Subband Coding Algorithm
Subband Coding Algorithm
The three major components of this system are  the analysis and synthesis filters,
 the bit allocation scheme, and
 the encoding scheme.
A substantial amount of research has focused on
each of these components.
(1) Analysis
Source output  analysis filter bank  subsampled encoded.
Analysis Filter Bank
 The source output is passed through a bank
of filters.
 This filter bank covers the range of
frequencies that make up the source output.
 The passband of each filter specifies each
set of frequencies that can pass through.
Subband Coding Algorithm
(1) Analysis
Source output  analysis filter bank  subsampled encoded.
Analysis Filter Bank
Decimation
 The outputs of the filters are subsampled
thus reducing the number of samples.
(1) Analysis
Source output  analysis filter bank  subsampled encoded.
Analysis Filter Bank
Decimation
 The justification for the subsampling is the
Nyquist rule and its extension justifies this
downsampling.
(1) Analysis
Source output  analysis filter bank  subsampled encoded.
Analysis Filter Bank
Decimation
 The amount of decimation depends on the
ratio of the bandwidth of the filter output to
the filter input.
Subband Coding Algorithm
(1) Analysis
Source output  analysis filter bank  subsampled encoded.
Analysis Filter Bank
Decimation
Encoding
 The decimated output is encoded using one
of several encoding schemes, including
ADPCM, PCM, and vector quantization.
(2) Quantization and Coding
 Selection of the compression scheme
 Allocation of bits between the subbands
allocate the available bits among the
subbands according to measure of the
information content in each subband.
This bit allocation procedure significantly
impacts quality of the final reconstruction.
Bit Allocation
Minimizing the distortion i.e. minimizing
the reconstruction error drives the bit
allocation procedure.
Different subbandsdifferent amount of
information.
Bit allocation procedure can have a
significant impact on the quality of the
final reconstruction
(3) Synthesis
 Quantized and Coded coefficients are used
to reconstruct a representation of the
original signal at the decoder.
Encoded samples from each subband
decoded upsampled  bank of
reconstruction filters outputs combined
 Final reconstructed output
Application
The subband coding algorithm has
applications in -
Speech Coding
Audio Coding
Image Compression
Application to Image Compression
LL
LH
HL
HH
Example 14.12.2 –
Image
Decomposing and
Example 14.12.2 –
Image
Decomposing and
Example 14.12.2 –
Image
Decomposing and
Coding the Subbands
LL
LH
DPCM
Discard
HL
SQ
HH
Some bands  VQ
Example 14.12.3 –
Coding the Subbands
Example 14.12.3 –
Coding the Subbands
Coding the Subbands
LL
LH
DPCM
Discard
HL
SQ
HH
Some bands  VQ
Summary
Subband coding is another approach to
decompose the source output into
components based on frequency.
Each of these components can then be
encoded using one of the techniques
described in the previous chapters.
Summary
The general subband encoding procedure can
be summarized as follows:
• Select a set of filters for decomposing the
source.
• Using the filters, obtain the subband signals.
• Decimate the output of the filters.
• Encode the decimated output.
The decoding procedure is the inverse of the
encoding procedure.