Start Scalar Quantizer Design Tool (SQDTool) to design scalar quantizer using Lloyd algorithm

Quantizers

`dspquant2`

Double-click on the Scalar Quantizer Design block to start SQDTool, a GUI that allows you to design and implement a scalar quantizer. Based on your input values, SQDTool iteratively calculates the codebook values that minimize the mean squared error until the stopping criteria for the design process is satisfied. The block uses the resulting quantizer codebook values and boundary points to implement your scalar quantizer encoder and/or decoder.

For the **Training Set** parameter, enter a set of observations, or
samples, of the signal you want to quantize. This data can be any variable defined in
the MATLAB^{®} workspace including a variable created using a MATLAB function, such as the default value
`randn(10000,1)`

.

You have two choices for the **Source of initial codebook
**parameter. Select `Auto-generate`

to have the block
choose the values of the initial codebook vector. In this case, the minimum training set
value becomes the first codeword, and the maximum training set value becomes the last
codeword. Then, the remaining initial codewords are equally spaced between these two
values to form a codebook vector of length N, where N is the **Number of
levels** parameter. When you select ```
User
defined
```

, enter the initial codebook values in the **Initial
codebook** field. Then, set the **Source of initial boundary
points** parameter. You can select `Mid-points`

to
locate the boundary points at the midpoint between the codewords. To calculate the
mid-points, the block internally arranges the initial codebook values in ascending
order. You can also choose `User defined`

and enter your own
boundary points in the **Initial boundary points (unbounded)** field.
Only one boundary point can be located between two codewords. When you select
`User defined `

for the **Source of initial boundary
points **parameter, the values you enter in the **Initial
codebook** and **Initial boundary points (unbounded)**
fields must be arranged in ascending order.

This block assumes that you are designing an unbounded quantizer. Therefore, the
first and last boundary points are always `-inf`

and
`inf`

regardless of any other boundary point values you might
enter.

After you have specified the quantization parameters, the block performs an iterative process to design the optimal scalar quantizer. Each step of the design process involves using the Lloyd algorithm to calculate codebook values and quantizer boundary points. Then, the block calculates the squared quantization error and checks whether the stopping criteria has been satisfied.

The two possible options for the **Stopping criteria** parameter are
`Relative threshold`

and ```
Maximum
iteration
```

. When you want the design process to stop when the
fractional drop in the squared quantization error is below a certain value, select
`Relative threshold`

. Then, for **Relative
threshold**, type the maximum acceptable fractional drop. When you want the
design process to stop after a certain number of iterations, choose ```
Maximum
iteration
```

. Then, enter the maximum number of iterations you want the
block to perform in the **Maximum iteration** field. For
**Stopping criteria**, you can also choose ```
Whichever
comes first
```

and enter a **Relative threshold
**and** Maximum iteration **value. The block stops
iterating as soon as one of these conditions is satisfied.

With each iteration, the block quantizes the training set values based on the newly
calculated codebook values and boundary points. When the training point lies on a
boundary point, the algorithm uses the **Tie-breaking rules** parameter
to determine which region the value is associated with. When you want the training point
to be assigned to the lower indexed region, select ```
Lower indexed
codeword
```

. To assign the training point with the higher indexed region,
select `Higher indexed codeword`

.

The **Searching methods** parameter determines how the block compares
the training points to the boundary points. Select ```
Linear
search
```

and SQDTool compares each training point to each quantization
region sequentially. This process continues until all the training points are associated
with the appropriate regions.

Select `Binary search `

for the **Searching methods
**parameter and the block compares the training point to the middle value of
the boundary points vector. When the training point is larger than this boundary point,
the block discards the lower boundary points. The block then compares the training point
to the middle boundary point of the new range, defined by the remaining boundary points.
This process continues until the training point is associated with the appropriate
region.

Click **Design and Plot** to design the quantizer with the
parameter values specified on the left side of the GUI. The performance curve and the
staircase character of the quantizer are updated and displayed in the figures on the
right side of the GUI.

You must click **Design and Plot** to apply any changes you
make to the parameter values in the SQDTool dialog box.

SQDTool can export parameter values that correspond to the figures displayed in the
GUI. Click the **Export Outputs** button, or press
**Ctrl+E**, to export the **Final Codebook**,
**Final Boundary Points**, and **Error** values to
the workspace, a text file, or a MAT-file. The **Error** values
represent the mean squared error for each iteration.

In the **Model** section of the GUI, specify the destination of
the block that will contain the parameters of your quantizer. For
**Destination**, select `Current model`

to
create a block with your parameters in the model you most recently selected. Type
`gcs`

in the MATLAB Command Window to display the name of your current model. Select
`New model`

to create a block in a new model file.

From the **Block type** list, select
`Encoder`

to design a Scalar Quantizer Encoder block.
Select `Decoder`

to design a Scalar Quantizer Decoder block.
Select `Both`

to design a Scalar Quantizer Encoder block and a
Scalar Quantizer Decoder block.

In the **Encoder block name** field, enter a name for the Scalar
Quantizer Encoder block. In the **Decoder block name** field, enter a
name for the Scalar Quantizer Decoder block. When you have a Scalar Quantizer Encoder
and/or Decoder block in your destination model with the same name, select the
**Overwrite target block(s)** check box to replace the block's
parameters with the current parameters. When you do not select this check box, a new
Scalar Quantizer Encoder and/or Decoder block is created in your destination
model.

Click **Generate Model**. SQDTool uses the parameters that
correspond to the current plots to set the parameters of the Scalar Quantizer Encoder
and/or Decoder blocks.

**Training Set**Enter the samples of the signal you would like to quantize. This data set can be a MATLAB function or a variable defined in the MATLAB workspace. The typical length of this data vector is

`1e6`

.**Source of initial codebook**Select

`Auto-generate`

to have the block choose the initial codebook values. Select`User defined`

to enter your own initial codebook values.**Number of levels**Enter the length of the codebook vector. For a b-bit quantizer, the length should be

*N*= 2^{b}.**Initial codebook**Enter your initial codebook values. From the

**Source of initial codebook**list, select`User defined`

in order to activate this parameter.**Source of initial boundary points**Select

`Mid-points`

to locate the boundary points at the midpoint between the codebook values. Choose`User defined`

to enter your own boundary points. From the**Source of initial codebook**list, select`User defined`

in order to activate this parameter.**Initial boundary points (unbounded)**Enter your initial boundary points. This block assumes that you are designing an unbounded quantizer. Therefore, the first and last boundary point are

`-inf`

and`inf`

, regardless of any other boundary point values you might enter. From the**Source of initial boundary points**list, select`User defined`

in order to activate this parameter.**Stopping criteria**Choose

`Relative threshold`

to enter the maximum acceptable fractional drop in the squared quantization error. Choose`Maximum iteration`

to specify the number of iterations at which to stop. Choose`Whichever comes first`

and the block stops the iteration process as soon as the relative threshold or maximum iteration value is attained.**Relative threshold**Type the value that is the maximum acceptable fractional drop in the squared quantization error.

**Maximum iteration**Enter the maximum number of iterations you want the block to perform. From the

**Stopping criteria**list, select`Maximum iteration`

in order to activate this parameter.**Searching methods**Choose

`Linear search`

to use a linear search method when comparing the training points to the boundary points. Choose`Binary search`

to use a binary search method when comparing the training points to the boundary points.**Tie-breaking rules**When a training point lies on a boundary point, choose

`Lower indexed codeword`

to assign the training point to the lower indexed quantization region. Choose`Higher indexed codeword`

to assign the training point to the higher indexed region.**Design and Plot**Click this button to display the performance curve and the staircase character of the quantizer in the figures on the right side of the GUI. These plots are based on the current parameter settings.

You must click

**Design and Plot**to apply any changes you make to the parameter values in the SQDTool GUI.**Export Outputs**Click this button, or press

**Ctrl+E**, to export the**Final Codebook**,**Final Boundary Points**, and**Error**values to the workspace, a text file, or a MAT-file.**Destination**Choose

`Current model`

to create a Scalar Quantizer block in the model you most recently selected. Type`gcs`

in the MATLAB Command Window to display the name of your current model. Choose`New model`

to create a block in a new model file.**Block type**Select

`Encoder`

to design a Scalar Quantizer Encoder block. Select`Decoder`

to design a Scalar Quantizer Decoder block. Select`Both`

to design a Scalar Quantizer Encoder block and a Scalar Quantizer Decoder block.**Encoder block name**Enter a name for the Scalar Quantizer Encoder block.

**Decoder block name**Enter a name for the Scalar Quantizer Decoder block.

**Overwrite target block(s)**When you do not select this check box and a Scalar Quantizer Encoder and/or Decoder block with the same block name exists in the destination model, a new Scalar Quantizer Encoder and/or Decoder block is created in the destination model. When you select this check box and a Scalar Quantizer Encoder and/or Decoder block with the same block name exists in the destination model, the parameters of these blocks are overwritten by new parameters.

**Generate Model**Click this button and SQDTool uses the parameters that correspond to the current plots to set the parameters of the Scalar Quantizer Encoder and/or Decoder blocks.

Gersho, A. and R. Gray. *Vector Quantization and Signal
Compression*. Boston: Kluwer Academic Publishers, 1992.

Double-precision floating point

Quantizer | Simulink |

Scalar Quantizer Decoder | DSP System Toolbox |

Scalar Quantizer Encoder | DSP System Toolbox |

Uniform Encoder | DSP System Toolbox |

Uniform Decoder | DSP System Toolbox |