Subband Coding (1)

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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 compressionscheme exactly suited to the source

output.



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.



Example 14.2.1

Xn

Zn

Yn

Zn

YnCompression

Scheme 1

Compression

Scheme 2

Xn



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 certainfrequencies.

(i) Low Pass Filters

(ii) High Pass Filters

(iii) Band Pass Filters



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.



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



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



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



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.



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




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 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.



(1) Analysis


sampled encoded.

Analysis Filter BankDecimation

The outputs of the filters are subsampled

thus reducing the number of samples.



(1) Analysis


sampled encoded.


The justification for the subsampling is the

Nyquist rule and its extension justifies thisdownsampling.



(1) Analysis


sampled encoded.


The amount of decimation depends on the

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



(1) Analysis


sampled encoded.


Encoding

The decimated output is encoded using oneof 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 thesubbands according to measure of theinformation content in each subband.

This bit allocation procedure significantlyimpacts quality of the final reconstruction.



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



(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 – Decomposing and

Image




Image



Coding the Subbands

SQ

LL LH

HL HH

DiscardDPCM

Some bands VQ



Example 14.12.3 – Coding the Subbands



Coding the Subbands

SQ

LL LH

HL HH

DiscardDPCM

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

Subband Coding (1)

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