Vector Quantizer Encoder
Index of nearest codeword based on Euclidean or weighted Euclidean distance measure
Libraries:
DSP System Toolbox /
Quantizers
Description
The Vector Quantizer Encoder block compares each input column vector to the codeword vectors in the codebook matrix. Each column of this codebook matrix is a codeword. The block finds the codeword vector nearest to the input column vector and returns its zero-based index. This block supports real floating-point and fixed-point signals on all input ports.
The Vector Quantizer Encoder block accepts real floating-point and fixed-point inputs. For more information, see the Ports section.
Ports
Input
U — Input data values
vector | matrix
Specify the input data values as a vector or a matrix.
The data, codebook values, and weighting factor inputs must have the same data type whenever they are present.
If the input is fixed point, it must be a signed integer or a signed fixed point value with a power-of-two slope and zero bias.
Data Types: single
| double
| int8
| int16
| int32
| fixed point
C — Codebook values
vector | matrix
Specify the codebook values as a k-by-N matrix, where k ≥ 1 and N ≥ 1. Each input column vector is compared to this codebook. Each column of the codebook matrix is a codeword, and each codeword has an index value. The first codeword vector corresponds to an index value of 0, the second codeword vector corresponds to an index value of 1, and so on.
The input data, codebook values, and weighting factor must be of the same data type.
If the codebook values are fixed-point, they must be signed values only.
Dependencies
To enable this port, set the Source of
codebook parameter to Input
port
.
Data Types: single
| double
| int8
| int16
| int32
| fixed point
W — Weighting factor
vector
Use the Weighting factor parameter to emphasize or deemphasize certain input values when calculating the distortion measure. For more information, see Weighting factor.
The input data, codebook values, and weighting factor must be of the same data type.
If the weighting factor is fixed-point, it must be signed values only.
Dependencies
To enable this port, set the Distortion measure parameter to
Weighted squared error
and the
Source of weighting factor parameter to
Input port
.
Data Types: single
| double
| int8
| int16
| int32
| fixed point
Output
I — Index values
scalar | row vector
Index values of the nearest codeword based on Euclidean or weighted Euclidean distance measure, returned as a scalar or a row vector.
Data Types: int8
| int16
| int32
| uint8
| uint16
| uint32
Q(U) — Output codeword
vector | matrix
Output codeword, returned as a vector or a matrix.
The block assigns the data type of the output codewords based on the data type of the input data. If the output codeword is fixed-point, it must be signed values only.
Data Types: single
| double
| int8
| int16
| int32
| fixed point
D — Quantization error
scalar | row vector
Quantization error, returned as a scalar or a row vector.
The block assigns the data type of the quantization error based on the data type of the input data. If the quantization error is fixed-point, it must be signed values only.
Data Types: single
| double
| int8
| int16
| int32
| fixed point
Parameters
Main Tab
Source of codebook — Source of codebook
Specify via dialog
(default) | Input port
Specify the source of codebook as one of these options:
Specify via dialog
–– Specify codebook values in the Codebook parameter.Input port
–– Specify codebook values through the input port C.
Codebook — Codebook values
[1.5 13.3 136.4 6.8 ; 2.5 14.3 137.4 7.8; 3.5
15.3 138.4 8.8]
(default)
Specify the codebook values as a k-by-N matrix, where k ≥ 1 and N ≥ 1. Each input column vector is compared to this codebook. Each column of the codebook matrix is a codeword, and each codeword has an index value. The first codeword vector corresponds to an index value of 0, the second codeword vector corresponds to an index value of 1, and so on. The codeword vectors must have the same number of rows as the input, U.
Dependencies
To enable this parameter, set the Source of
codebook parameter to Specify via
dialog
.
Distortion measure — Measure of distortion
Squared error
(default) | Weighted squared error
Specify the measure of distortion as one of these:
Squared error
–– Block calculates the distortion by evaluating the Euclidean distance between the input column vector and each codeword in the codebook.Weighted squared error
–– Block calculates the distortion by evaluating a weighted Euclidean distance using a weighting factor to emphasize or deemphasize certain input values.
Source of weighting factor — Source of weighting factor
Specify via dialog
(default) | Input port
Specify the source of weighting factor as one of these options:
Specify via dialog
–– Specify the weighting factor in the Weighting factor parameter of the block dialog box.Input port
–– Specify the weighting factor through the input port W.
Dependencies
To enable this parameter, set the Distortion
measure parameter to Weighted squared
error
.
Weighting factor — Weighting factor
[1 1 1]
(default) | vector
Specify weighting factor as a vector of values. The length of this vector must equal the number of rows of the input, U.
Use the Weighting factor parameter to emphasize
or deemphasize certain input values when calculating the distortion
measure. For example, consider the p-th input column
vector, . When you want to neglect the effect of the first
element of this vector, enter [0 1 1 ... 1]
as the
Weighting factor parameter. This weighting
factor is used to calculate the weighted squared error using the
equation:
Because of the weighting factor used in this example, the weighted squared error is not affected by the first element of the input matrix. Therefore, the first element of the input column vector no longer impacts the choice of index value output by the Vector Quantizer Encoder block.
Dependencies
To enable this parameter, set the Source of weighting
factor parameter to Specify via
dialog
.
Tie-breaking rule — Tie-breaking rule
Choose the lower
index
(default) | Choose the higher index
Set this parameter to determine the behavior of the block when an
input column vector is equidistant from two codewords. When you want the
input column vector to be represented by the lower index valued
codeword, select Choose the lower index
. To
represent the input column vector by the higher index valued codeword,
select Choose the higher index
.
Output codeword — Output codeword
off
(default) | on
Select the Output codeword check box to output at port Q(U) the codeword vectors that correspond to each index value. When the input is a matrix, the corresponding codeword vectors are horizontally concatenated into a matrix.
Output quantization error — Output quantization error
off
(default) | on
Select the Output quantization error check box to output at port D the quantization error that results when the block represents the input column vector by its nearest codeword. When the input is a matrix, the quantization error values are horizontally concatenated.
Index output data type — Index output data type
int32
(default) | int8
| uint8
| int16
| uint16
| uint32
| Inherit via back propagation
Specify the data type of the index output from the block at port I as one of the following:
int8
uint8
int16
uint16
int32
uint32
To inherit the index output data type, select Inherit via
back propagation
.
Data Types Tab
Rounding mode — Rounding mode
Floor
(default) | Ceiling
| Convergent
| Nearest
| Round
| Simplest
| Zero
Specify the rounding mode for fixed-point operations as one of the following:
Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero
For more details, see rounding mode.
Saturate on integer overflow — Saturate on integer overflow
off
(default) | on
When you select this parameter, the block saturates the result of its fixed-point operation. When you clear this parameter, the block wraps the result of its fixed-point operation. For details, see overflow mode for fixed-point operations.
Product output — Product output data type
Same as input
(default) | Binary point scaling
As depicted above, the output of the multiplier is placed into the product output data type and scaling. Use this parameter to specify how you would like to designate this product output word and fraction lengths.
When you select
Same as input
, these characteristics match those of the input to the block.When you select
Binary point scaling
, you can enter the word length and the fraction length of the product output in bits.
Word length — Product output word length
16
(default) | positive integer in range [2,128]
Specify the product output word length as a positive integer in the range [2,128].
Dependencies
To enable this parameter, set the Product
output parameter to Binary point
scaling
.
Fraction length — Product output fraction length
15
(default) | integer
Specify the product output fraction length as an integer.
Dependencies
To enable this parameter, set the Product
output parameter to Binary point
scaling
.
Accumulator — Accumulator data type
Same as product
output
(default) | Same as input
| Binary point scaling
As depicted in this diagram, inputs to the accumulator are cast to the accumulator data type. The output of the adder remains in the accumulator data type as each element of the input is added to it. Use this parameter to specify how you would like to designate the accumulator word and fraction lengths.
When you select
Same as product output
, these characteristics match those of the product output.When you select
Same as input
, these characteristics match those of the input to the block.When you select
Binary point scaling
, you can enter the word length and the fraction length of the accumulator in bits.
Word length — Accumulator word length
16
(default) | positive integer in range [2,128]
Specify the accumulator word length as a positive integer in the range [2,128].
Dependencies
To enable this parameter, set the Accumulator
parameter to Binary point scaling
.
Fraction length — Accumulator fraction length
15
(default) | integer
Specify the accumulator fraction length as an integer.
Dependencies
To enable this parameter, set the Accumulator
parameter to Binary point scaling
.
Block Characteristics
Data Types |
|
Direct Feedthrough |
|
Multidimensional Signals |
|
Variable-Size Signals |
|
Zero-Crossing Detection |
|
More About
Data Type Support
The input data values, codebook values, and weighting factor values are input to the block
at ports U, C, and W, respectively. The data type of the input data values, codebook
values, and weighting factor values can be double
,
single
, or fixed point. The input data, codebook
values, and weighting factor must be of the same data type.
The outputs of the block are the index values, output codewords, and quantization error.
Use the Index output data type parameter to specify the data
type of the index output from the block at port I. The data type of the index can be
int8
, uint8
,
int16
, uint16
,
int32
, or uint32
. The data
type of the output codewords and the quantization error can be
double
, single
, or fixed
point. The block assigns the data type of the output codewords and the quantization
error based on the data type of the input data.
Fixed-Point Data Types
This diagram shows the data types used within the Vector Quantizer Encoder block for fixed-point signals.
You can set the product output, accumulator, and index output data types in the block dialog box.
Algorithms
The block finds the nearest codeword by calculating the distortion. The block uses two methods for calculating distortion –– Euclidean squared error (unweighted) and weighted Euclidean squared error. Consider the codebook . This codebook has N codewords and each codeword has k elements. The i-th codeword is defined as a column vector, . The multichannel input has M columns and is defined as , where the p-th input column vector is .
The squared error (unweighted) is calculated using the equation
The weighted squared error is calculated using the equation
where the weighting factor is defined as . The index of the codeword that is associated with the minimum distortion is assigned to the input column vector.
References
[1] Gersho, A. and R. Gray. Vector Quantization and Signal Compression. Boston: Kluwer Academic Publishers, 1992.
Extended Capabilities
C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.
Generated code relies on the memcpy
or
memset
function (string.h
) under certain
conditions.
Version History
Introduced before R2006a
See Also
Quantizer (Simulink) | Scalar Quantizer Decoder | Uniform Encoder | Uniform Decoder | Vector Quantizer Decoder
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