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Subband Coding
Jennie Abraham
07/23/2009
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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
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Overview – cont’d
Source data characteristics -
Unfortunately, most source outputs
exhibit a combination of characteristics.
difficult to select a compressionscheme exactly suited to the source
output.
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Overview - cont’d
Decomposing the source output into
constituent parts using some method.
Each constituent part is encoded usingone or more of the methods described
previously.
enables the use of these compression
schemes more effectively.
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Example 14.2.1
Xn
Zn
Yn
Zn
YnCompression
Scheme 1
Compression
Scheme 2
Xn
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Example 14.2.1 – Cont’d
Xn = 10 14 10 12 14 8 14 12 10 8 10 12
Yn =
Xn = Yn + Zn
Zn =
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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.
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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.
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Filters
A filter is system that isolates certainfrequencies.
(i) Low Pass Filters
(ii) High Pass Filters
(iii) Band Pass Filters
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Digital Filters
Sampling and Nyquist rule :
If fo is the highest frequency of the signal then thesampling 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.
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Digital Filtering
The general form of the input-outputrelationships 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
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Example 14.3.1
Filter Coefficients ao = 1.25, a1= 0.5 and theinput sequence {Xn} is given by –
then the output {Yn} is given by
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Example 14.3.2
Consider a filter with a o = 1 and b 1 = 2.
The input sequence is a 1 followed by 0s.
Then the output is
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Filters in literature
Design and analysis of digital filters isdetailed in Sections 14.5-14.8 of thetextbook.
A useful approach is to make use of the available literature to select thenecessary filters rather than designthem.
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Filters used in Subband Coding
Couple of examples of –
Quadrature Mirror Filters (QMF),
Johnston Filter
Smith-Barnwell Filters
Daubechies Filters
….and so on
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8-tap Johnston Low-Pass Filter
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8-tap Johnston Low-Pass Filter
LP
HP
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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.
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Subband Coding Algorithm
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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.
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(1) Analysis
Source output analysis filter bank sub-
sampled 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.
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Subband Coding Algorithm
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(1) Analysis
Source output analysis filter bank sub-
sampled encoded.
Analysis Filter BankDecimation
The outputs of the filters are subsampled
thus reducing the number of samples.
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(1) Analysis
Source output analysis filter bank sub-
sampled encoded.
Analysis Filter BankDecimation
The justification for the subsampling is the
Nyquist rule and its extension justifies thisdownsampling.
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(1) Analysis
Source output analysis filter bank sub-
sampled encoded.
Analysis Filter BankDecimation
The amount of decimation depends on the
ratio of the bandwidth of the filter output tothe filter input.
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(1) Analysis
Source output analysis filter bank sub-
sampled encoded.
Analysis Filter BankDecimation
Encoding
The decimated output is encoded using oneof several encoding schemes, including
ADPCM, PCM, and vector quantization.
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(2) Quantization and Coding
Selection of the compression scheme
Allocation of bits between the subbands
allocate the available bits among thesubbands according to measure of theinformation content in each subband.
This bit allocation procedure significantlyimpacts quality of the final reconstruction.
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Bit Allocation
Minimizing the distortion i.e. minimizing
the reconstruction error drives the bit
allocation procedure.
Different subbandsdifferent amount of
information.
Bit allocation procedure can have a
significant impact on the quality of the
final reconstruction
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(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
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Application
The subband coding algorithm has
applications in -
Speech Coding
Audio Coding
Image Compression
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Application to Image Compression
LL LH
HL HH
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Example 14.12.2 – Decomposing and
Image
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Example 14.12.2 – Decomposing and
Image
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Example 14.12.2 – Decomposing and
Image
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Coding the Subbands
SQ
LL LH
HL HH
DiscardDPCM
Some bands VQ
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Example 14.12.3 – Coding the Subbands
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Example 14.12.3 – Coding the Subbands
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Coding the Subbands
SQ
LL LH
HL HH
DiscardDPCM
Some bands VQ
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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.
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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