subband coding
DESCRIPTION
Subband Coding. Jennie Abraham 07/23/2009. Overview. Previously, different compression schemes were looked into – Vector Quantization Scheme Differential Encoding Scheme Scalar Quantization Scheme - Most efficient when the data exhibit certain characteristics. Overview – cont’d. - PowerPoint PPT PresentationTRANSCRIPT
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
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 certain frequencies.
(i) Low Pass Filters(ii) High Pass Filters(iii) 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 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.
Subband Coding Algorithm
(1) Analysis
Source output analysis filter bank sub-sampled 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 sub-sampled 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 sub-sampled 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 sub-sampled 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 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 CodingAudio CodingImage Compression
Application to Image Compression
LL LH
HL HH
Example 14.12.2 – Decomposing and Image
Example 14.12.2 – Decomposing and Image
Example 14.12.2 – Decomposing and Image
Coding the Subbands
SQ
LL LH
HL HH
DiscardDPCM
Some bands VQ
Example 14.12.3 – Coding the Subbands
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 encoding procedure.