EEM 517 - Veri Sıkıştırma
Subband Coding
Yrd. Doç. Dr. Derya Yılmaz
The Jennie Abraham’s presentation (www-ee.uta.edu) has been revised with many new slides.
Some compression schemes are:
(i)Vector Quantization Scheme
(ii)Differential Encoding Scheme
(iii)Scalar Quantization Scheme
Most efficient when the data exhibit certain
characteristics
Source data characteristics
Most source outputs exhibit a combination of
characteristics.
Difficult to select a compression scheme
exactly suited to the source output.
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.
Yn
Compression
Scheme 1
Yn
Xn
Xn
Compression
Zn
Scheme 2
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.



Low Pass Filters
High Pass Filters
Band Pass Filters
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.
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
Filter Coefficients ao = 1.25, a1= 0.5 and the input
sequence {Xn} is given by –
then the output {Yn} is given by
This output is called the impulse response of the filter.
The impulse response sequence is usually represented
by {hn}. Therefore, for this filter we would say that
If we know the impulse response we also know the
values of ai. Knowledge of the impulse response
completely specifies the filter.
Because the impulse response goes to zero after a
finite number of samples (two in this case), the filter
is an FIR filter.
Consider a filter with ao = 1 and b1 = 0.9
The input sequence is a 1 followed by 0s.
Then the output is
The impulse response can be written more
compactly as
Notice that the impulse response is nonzero
for all n > 0, which makes this an IIR filter.
Filters used in Subband Coding
Couple of examples of

Quadrature Mirror Filters (QMF),

Johnston Filter

Smith-Barnwell Filters

Daubechies Filters
Filter Bank
•What we do with these
filters in subband coding is
that we construct a filter bank
like shown in the figure.
•The most frequently used
filter banks in subband
coding consist of a cascade
of stages, where each stage
consists of a low-pass filter
and a high-pass filter.
•Here we see that the coefficients are symmetric.
We can employ it as both low pass and high pass.
•Here we can see clearly how the filter coefficients can be
made to work as low pass and high pass.
The filters with fewer taps are less efficient in their
decomposition than the filters with more taps. The number
of taps dictates the number of multiply-add operations
necessary to generate the filter outputs.
Thus, if we want to obtain more efficient decompositions,
we do so by increasing the amount of computation.
Analysis
Source
output

Analysis
filter bank

Subsampled

Encoded
Analysis Filter Bank
Decimation (Downsampling)
The outputs of the filters are subsampled thus
reducing the number of samples.
We can reduce the number of samples at the output of the filter because the
range of frequencies at the output of the filter is less than the range of frequencies at
the input to the filter. This process of reducing the number of samples is called
decimation or downsampling.
The amount of decimation depends on the ratio of the bandwidth of the filter output
to the filter input. If the bandwidth at the output of the filter is 1/M of the bandwidth
at the input to the filter, we would decimate the output by a factor of M by keeping
every Mth sample. The symbol M is used to denote this decimation.
Encoding
The decimated output is encoded using one of
several encoding schemes, including ADPCM,
PCM, and vector quantization.
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.
Synthesis
Quantized and Coded coefficients are used to
reconstruct a representation of the original signal
at the decoder.
Encoded
Bank of
ReUpsamples 
Outputs
 reconstruction 
 constructed
Decoded 
sampled
combined
from each
filters
output
subband
Application
The subband coding algorithm has applications
in 


Speech Coding
Audio Coding
Image Compression
Advantages of subband coding:
 They operate on the whole image as one single
block, thus avoiding blocking artifacts while
dynamically adjusting the spatial/frequency
resolution to the appropriate level in various
regions of the image.
 In practice, this coding performs as well as DCT
and sometimes better, especially at low bitrate.