Sub-Band Coding

Multimedia Systems and StandardsS2 IF Telkom University

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OverviewCompression schemes were efficient

when the data exhibit certain characteristics.

Unfortunately, most source outputs exhibit a combination of characteristics.

difficult to select a compression scheme exactly suited to the source output.

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Now, these compression techniques as you know by now, are most efficient when the data exhibit some predominant characteristic.

1.If the source output is truly random, it is best to use scalar quantization.

2.The vector quantization scheme is most effective if blocks of the source output show a high degree of clustering.

3.The differential encoding scheme is most effective when the sample-to-sample difference is small.

Thus, if a source exhibited certain well-defined characteristics, we could choose a compression scheme most suited to that characteristic.

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Overview - cont’dDecomposing 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.

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Example

Xn

Zn

Yn

Zn

YnCompression Scheme 1

Compression Scheme 2

Xn

Video Compression

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Laye

red

Cod

er D

D

D

+

+

Layer 0

Layer 1

Layer 2 1 Mb/s

256 kb/s

64 kb/s

Layered video encoding/decoding. D denotes the decoder.

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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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FiltersA filter is system that isolates

certain frequencies.

(i) Low Pass Filters(ii)High Pass Filters(iii)Band Pass Filters

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Filters – Cont’dFilter 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.

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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 = 2f2 per second.

Violation of Nyquist rule: Distortion due to aliasing.

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Digital FilteringThe 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

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Example Filter Coefficients ao = 1.25, a1= 0.5

and the input sequence {Xn} is given by –

then the output {Yn} is given by

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ExampleConsider a filter with ao = 1 and b1

= 2. The input sequence is a 1 followed

by 0s. Then the output is

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Filters used in Subband Coding

Couple of examples of –Quadrature Mirror Filters (QMF),Johnston FilterSmith-Barnwell FiltersDaubechies Filters

….and so on

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Filter BanksSubband 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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(1) AnalysisSource output analysis filter bank sub-

sampled encoded.

Analysis Filter BankThe 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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(1) AnalysisSource output analysis filter bank

sub-sampled encoded.

Analysis Filter Bank DecimationThe outputs of the filters are

subsampled thus reducing the number of samples.

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(1) AnalysisSource output analysis filter bank

sub-sampled encoded.

Analysis Filter Bank DecimationThe justification for the subsampling is

the Nyquist rule and its extension justifies this downsampling.

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(1) AnalysisSource output analysis filter bank

sub-sampled encoded.

Analysis Filter BankDecimationThe amount of decimation depends on

the ratio of the bandwidth of the filter output to the filter input.

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(1) AnalysisSource output analysis filter bank sub-

sampled encoded.

Analysis Filter BankDecimationEncodingThe decimated output is encoded using

one of 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 the subbands according to measure of the information content in each subband.

This bit allocation procedure significantly impacts quality of the final reconstruction.

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Bit AllocationMinimizing 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) SynthesisQuantized 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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ApplicationThe subband coding algorithm has

applications in -

Speech CodingAudio CodingImage Compression

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Application to Image Compression

LL LH

HL HH

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Decomposing and Image

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Decomposing and Image

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Decomposing and Image

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Coding the Subbands

SQ

LL LH

HL HH

DiscardDPCM

Some bands VQ

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Coding the Subbands

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Coding the Subbands

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SummarySubband 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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SummaryThe 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.

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Example – Cont’d

Xn = 10 14 10 12 14 8 14 12 10 8 10 12

Yn =

Xn = Yn + Zn Zn =