quantiz
Produce quantization index and quantized output value
Syntax
Description
[
specifies index
,quants
] = quantiz(sig
,partition
,codebook
)codebook
, which prescribes a value for each partition in the
scalar quantization. codebook
is a vector whose length must exceed the
length of partition
by one. The function also returns
quants
, which contains the scalar quantization of
sig
and depends on the quantization levels and prescribed values in
the codebook.
Examples
Produce Quantization Index and Quantized Output Value
Show how the quantiz
function uses partition and codebook to map a real vector, samp
, to a new vector, quantized
, whose entries are either -1, 0.5, 2, or 3.
Generate sample data and specify partition
and codebook
vectors. Specify the partition
vector by defining the distinct endpoints of the different intervals as the element values of the vector. Specify the codebook
vector with an element value for each interval defined in the partition
vector. The codebook
vector must be one element longer than the partition
vector.
samp = [-2.4, -1, 0, 0.2, 0.8, 1.2, 2,3, 3.5, 5]; partition = [0, 1, 3]; codebook = [-1, 0.5, 2, 3];
Quantize the data samples. Display the input sample data, the quantization index, and the corresponding quantized output value of the input data.
[index,quantized] = quantiz(samp,partition,codebook); [samp; index; quantized]'
ans = 10×3
-2.4000 0 -1.0000
-1.0000 0 -1.0000
0 0 -1.0000
0.2000 1.0000 0.5000
0.8000 1.0000 0.5000
1.2000 2.0000 2.0000
2.0000 2.0000 2.0000
3.0000 2.0000 2.0000
3.5000 3.0000 3.0000
5.0000 3.0000 3.0000
Quantize Sampled Sine Wave
To illustrate the nature of scalar quantization, this example shows how to quantize a sine wave. Plot the original and quantized signals to contrast the x symbols that make up the sine curve with the dots that make up the quantized signal. The vertical coordinate of each dot is a value in the vector codebook.
Generate a sine wave sampled at times defined by t
. Specify the partition
input by defining the distinct endpoints of the different intervals as the element values of the vector. Specify the codebook
input with an element value for each interval defined in the partition
vector. The codebook vector must be one element longer than the partition vector.
t = [0:.1:2*pi]; sig = sin(t); partition = [-1:.2:1]; codebook = [-1.2:.2:1];
Perform quantization on the sampled sine wave.
[index,quants] = quantiz(sig,partition,codebook);
Plot the quantized sine wave and the sampled sine wave.
plot(t,sig,'x',t,quants,'.') title('Quantization of Sine Wave') xlabel('Time') ylabel('Amplitude') legend('Original sampled sine wave','Quantized sine wave'); axis([-.2 7 -1.2 1.2])
Optimize Quantization Parameters
Testing and selecting parameters for large signal sets with a fine quantization scheme can be tedious. One way to produce partition and codebook parameters easily is to optimize them according to a set of training data. The training data should be typical of the kinds of signals to be quantized.
This example uses the lloyds
function to optimize the partition and codebook according to the Lloyd algorithm. The code optimizes the partition and codebook for one period of a sinusoidal signal, starting from a rough initial guess. Then the example runs the quantiz
function twice to generate quantized data by using the initial partition
and codebook
input values and by using the optimized partitionOpt
and codebookOpt
input values. The example also compares the distortion for the initial and the optimized quantization.
Define variables for a sine wave signal and initial quantization parameters. Optimize the partition and codebook by using the lloyds
function.
t = 0:.1:2*pi; sig = sin(t); partition = -1:.2:1; codebook = -1.2:.2:1; [partitionOpt,codebookOpt] = lloyds(sig,codebook);
Generate quantized signals by using the initial and the optimized partition and codebook vectors. The quantiz
function automatically computes the mean square distortion and returns it as the third output argument. Compare mean square distortions for quantization with the initial and optimized input arguments to see how less distortion occurs when using the optimized quantized values.
[index,quants,distor] = quantiz(sig,partition,codebook);
[indexOpt,quantOpt,distorOpt] = ...
quantiz(sig,partitionOpt,codebookOpt);
[distor, distorOpt]
ans = 1×2
0.0148 0.0022
Plot the sampled sine wave, the quantized sine wave, and the optimized quantized sine wave.
plot(t,sig,'x',t,quants,'.',t,quantOpt,'s') title('Quantization of Sine Wave') xlabel('Time') ylabel('Amplitude') legend('Original sampled sine wave', ... 'Quantized sine wave', ... 'Optimized quantized sine wave'); axis([-.2 7 -1.2 1.2])
Input Arguments
sig
— Input signal
vector
Input signal, specified as a vector. This input specifies the sampled signal for this function to perform quantization.
Data Types: double
partition
— Distinct endpoints of different ranges
row vector
Distinct endpoints of different ranges, specified as a row vector. This input defines several contiguous, nonoverlapping ranges of values within the set of real numbers. The values present in this input must be strictly in ascending order. The length of this vector must be one less than the number of partition intervals.
Example: [0
, 1
, 3
]
partitions the input row vector into the four sets {X:
X ≤ 0
}, {X:
0
< X ≤ 1
},
{X: 1
< X ≤
3
}, and {X: 3 <
X}.
Data Types: double
codebook
— Quantization value for each partition
row vector
Quantization value for each partition, specified as a row vector. This input
prescribes a common value for each partition in the scalar quantization. The length of
this vector must equal the number of partition intervals, that is, the length of this
vector must exceed the length of the partition
input by one.
Data Types: double
Output Arguments
index
— Quantization index
nonnegative row vector
Quantization index of the input signal, returned as a nonnegative row vector. This
output determines on which partition interval, each input value is mapped. Each element
in index
is one of the N integers in the range
[0, N–1].
If the partition
input has length N,
index
is a vector whose Kth entry is:
0
ifsig
(K) ≤partition
(1
)M if
partition
(M) <sig
(K) ≤partition
(M+1)N if
partition
(N) ≤sig
(K
)
quants
— Output of quantizer
row vector
Output of the quantizer, which contains the quantization values of the input signal,
returned as a row vector. The size of quants
matches that of input
argument sig
. When codebook
is not specified
as an input argument, you can define the codebook values as a vector whose length must
exceed the length of the partition
by one.
quants
is calculated based on the codebook
and index
inputs and is given by
quants
(i) =
codebook
(index
(i) + 1), where
i is an integer in the range [1,
length(
].sig
)
distor
— Mean square distortion
positive scalar
Mean square distortion of the quantized signal, returned as a positive scalar. You
can reduce this distortion by choosing appropriate partition and codebook values. For
more information on optimizing partition and codebook values, see the lloyds
function.
Version History
Introduced before R2006a
See Also
Functions
lloyds
|dpcmenco
|dpcmdeco
|huffmanenco
|huffmandeco
|arithenco
|arithdeco
|compand
Topics
MATLAB Command
You clicked a link that corresponds to this MATLAB command:
Run the command by entering it in the MATLAB Command Window. Web browsers do not support MATLAB commands.
Select a Web Site
Choose a web site to get translated content where available and see local events and offers. Based on your location, we recommend that you select: .
You can also select a web site from the following list:
How to Get Best Site Performance
Select the China site (in Chinese or English) for best site performance. Other MathWorks country sites are not optimized for visits from your location.
Americas
- América Latina (Español)
- Canada (English)
- United States (English)
Europe
- Belgium (English)
- Denmark (English)
- Deutschland (Deutsch)
- España (Español)
- Finland (English)
- France (Français)
- Ireland (English)
- Italia (Italiano)
- Luxembourg (English)
- Netherlands (English)
- Norway (English)
- Österreich (Deutsch)
- Portugal (English)
- Sweden (English)
- Switzerland
- United Kingdom (English)