For given input, find index of nearest codeword based on Euclidean or weighted Euclidean distance measure
Quantizers
dspquant2
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 zerobased index. This block supports real floatingpoint and fixedpoint signals on all input ports.
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, $$CB=\left[\begin{array}{cccc}C{W}_{1}& C{W}_{2}& \mathrm{...}& C{W}_{N}\end{array}\right]$$. This codebook has N codewords; each codeword has k elements. The ith codeword is defined as a column vector, $$C{W}_{i}=\left[\begin{array}{cccc}{a}_{1i}& {a}_{2i}& \mathrm{...}& {a}_{ki}\end{array}\right]$$. The multichannel input has M columns and is defined as $$U=\left[\begin{array}{cccc}{U}_{1}& {U}_{2}& \mathrm{...}& {U}_{M}\end{array}\right]$$, where the pth input column vector is $${U}_{p}={\left[\begin{array}{cccc}{u}_{1p}& {u}_{2p}& \mathrm{...}& {u}_{kp}\end{array}\right]}^{\prime}$$. The squared error (unweighted) is calculated using the equation
$$D={\displaystyle \sum _{j=1}^{k}{\left({a}_{ji}{u}_{jp}\right)}^{2}}$$
The weighted squared error is calculated using the equation
$$D={\displaystyle \sum _{j=1}^{k}{w}_{j}{\left({a}_{ji}{u}_{jp}\right)}^{2}}$$
where the weighting factor is defined as $$W=\left[\begin{array}{cccc}{w}_{1}& {w}_{2}& \mathrm{...}& {w}_{k}\end{array}\right]$$. The index of the codeword that is associated with the minimum distortion is assigned to the input column vector.
You can select how you want to enter the codebook values using the Source of
codebook parameter. When you select Specify via
dialog
, you can type the codebook values into the block parameters
dialog box. Select Input port
and port C appears on the
block. The block uses the input to port C as the Codebook
parameter.
The Codebook parameter is an kbyN matrix of values, 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.
For the Distortion measure parameter, select Squared
error
when you want the block to calculate the distortion by
evaluating the Euclidean distance between the input column vector and each codeword in
the codebook. Select Weighted squared error
when you want to
use a weighting factor to emphasize or deemphasize certain input values.
For the Source of weighting factor parameter, select
Specify via dialog
to enter a weighting factor vector in
the dialog box. Choose Input port
to specify the weighting
factor using port W.
Use the Weighting factor parameter to emphasize or deemphasize
certain input values when calculating the distortion measure. For example, consider the
pth input column vector, $${U}_{p}$$, as previously defined. 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
$$D={\displaystyle \sum _{j=1}^{k}{w}_{j}{\left({a}_{ji}{u}_{jp}\right)}^{2}}$$
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.
Use the Index output data type parameter to specify the data type
of the index values output at port I. The data type of the index values can be
int8
, uint8
,
int16
, uint16
,
int32
, or uint32
.
When an input vector is equidistant from two codewords, the block uses the
Tiebreaking rule parameter to determine which index value the
block chooses. When you want the input 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
.
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.
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.
The Vector Quantizer Encoder block accepts real floatingpoint and fixedpoint inputs. For more information on the data types accepted by each port, see Data Type Support or Supported Data Types.
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
Fixedpoint. The input data, codebook values, and weighting factor must be 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
Fixedpoint. The block assigns the data type of the output codewords and the
quantization error based on the data type of the input data.
The following diagram shows the data types used within the Vector Quantizer Encoder block for fixedpoint signals.
You can set the product output, accumulator, and index output data types in the block dialog as discussed below.
Choose Specify via dialog
to type the
codebook values into the block parameters dialog box. Select
Input port
to specify the codebook values
using the block's input port, C.
Enter a kbyN matrix of values,
where 1 ≤ k
and 1 ≤ N, to which your input column vector or matrix is
compared. This parameter is visible if, from the Source of
codebook list, you select Specify via
dialog
.
Select Squared error
when you want the
block to calculate the distortion by evaluating the Euclidean distance
between the input column vector and each codeword in the codebook.
Select Weighted squared error
when you want
the block to calculate the distortion by evaluating a weighted Euclidean
distance using a weighting factor to emphasize or deemphasize certain
input values.
Select Specify via dialog
to enter a value
for the weighting factor in the dialog box. Choose Input
port
and specify the weighting factor using port W on
the block. This parameter is visible if, for the Distortion
measure parameter, you select Weighted
squared error
.
Enter a vector of values. This vector must have length equal to the
number of rows of the input, U. This parameter is visible if, for the
Source of weighting factor parameter, you
select Specify via dialog
.
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
.
Select this check box to output the codeword vectors nearest to the input column vectors.
Select this check box to output the quantization error value that results when the block represents the input column vector by the nearest codeword.
Select int8
,
uint8
, int16
,
uint16
, int32
,
or uint32
as the data type of the index
output at port I. To inherit the index output data type, select
Inherit via back propagation
.
Specify the rounding mode for fixedpoint operations as one of the following:
Floor
Ceiling
Convergent
Nearest
Round
Simplest
Zero
For more details, see rounding mode.
When you select this parameter, the block saturates the result of its
fixedpoint operation. When you clear this parameter, the block wraps
the result of its fixedpoint operation. For details on
saturate
and wrap
, see overflow
mode for fixedpoint operations.
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.
As depicted above, 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.
Gersho, A. and R. Gray. Vector Quantization and Signal Compression. Boston: Kluwer Academic Publishers, 1992.
Port  Supported Data Types 

U 

C 

W 

I 

Q(U) 

D 

Quantizer (Simulink)  Simulink 
Scalar Quantizer Decoder  DSP System Toolbox 
Scalar Quantizer Design  DSP System Toolbox 
Uniform Encoder  DSP System Toolbox 
Uniform Decoder  DSP System Toolbox 
Vector Quantizer Decoder  DSP System Toolbox 