Description

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.

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.

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.

Parameters

References

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

Supported Data Types

See Also