In the sections that follow, you build a
model that uses fixed-point parameters and local data in a Stateflow^{®} chart.
In this model, the chart acts as a low-pass Butterworth filter:

Building this model requires a Signal Processing Toolbox™ license.

In this section, you create a stateless flow chart that accepts one input and provides one output.

At the MATLAB

^{®}prompt, type`sfnew`

to create a new model with an empty chart.In your chart, add a flow chart with a single branch:

The values

`b0`

,`b1`

, and`a1`

are the coefficients of the low-pass Butterworth filter. For more information about the filter coefficients, see Define the Model Callback Function.Add the following data to your chart:

Data Name Scope Type `x`

`Input`

`Inherit:Same as Simulink`

`y`

`Output`

`fixdt(1,16,10)`

`x_n1`

`Local`

`fixdt(1,16,12)`

`y_n1`

`Local`

`fixdt(1,16,10)`

`b0`

`Parameter`

`fixdt(1,16,15)`

`b1`

`Parameter`

`fixdt(1,16,15)`

`a1`

`Parameter`

`fixdt(1,16,15)`

Save your model.

In this section, you define a preload callback for the model.
This callback function computes the values for `b0`

, `b1`

,
and `a1`

in the chart.

Open the Model Properties dialog box by selecting

**File**>**Model Properties**>**Model Properties**in the model window.In the

**Callbacks**tab, select**PreLoadFcn**.Enter the following MATLAB code for the preload function:

Fs = 1000; Fc = 50; [B,A] = butter(1,2*pi*Fc/(Fs/2)); b0 = B(1); b1 = B(2); a1 = A(2);

In the code:

The sampling frequency

`Fs`

is 1000 Hz.The cutoff frequency

`Fc`

is 50 Hz.The

`butter`

function constructs a first-order low-pass Butterworth filter with a normalized cutoff frequency of`(2*pi*Fc/(Fs/2))`

radians per second. The function output`B`

contains the numerator coefficients of the filter in descending powers of z. The function output`A`

contains the denominator coefficients of the filter in descending powers of z.

Click

**OK**to close the dialog box.Save your model.

In this section, you add the remaining blocks to the model.

Open the Simulink Library Browser.

From the Simulink/Sources library, add a Sine Wave block with the following parameter settings to the model:

Parameter Setting **Sine type**`Time based`

**Time**`Use simulation time`

**Amplitude**`1`

**Bias**`0`

**Frequency**`2*pi*Fc`

**Phase**`0`

**Sample time**`1/Fs`

**Interpret vector parameters as 1-D**`On`

The Sine Wave block provides the signal that you want to filter using the Stateflow chart. This block outputs a floating-point signal.

From the Simulink/Signal Attributes library, add a Data Type Conversion block with the following parameter settings to the model:

Parameter Setting **Output minimum**`[]`

**Output maximum**`[]`

**Output data type**`fixdt(1,16,14)`

**Lock output data type setting against changes by the fixed-point tools**`Off`

**Input and output to have equal**`Real World Value (RWV)`

**Integer rounding mode**`Floor`

**Saturate on integer overflow**`Off`

**Sample time**`-1`

The Data Type Conversion block converts the floating-point signal from the Sine Wave block to a fixed-point signal. By converting the signal to a fixed-point type, the model can simulate using less memory.

From the Simulink/Sinks library, add a Scope block to the model.

Connect and label the blocks as follows:

Close the Library Browser and save your model.

In this section, you specify solver and diagnostic options for simulation.

In the Stateflow Editor, select

**Simulation**>**Model Configuration Parameters**.In the

**Solver**pane, set the following parameters:Parameter Setting **Stop time**`0.1`

**Type**`Fixed-step`

**Solver**`discrete (no continuous states)`

**Fixed-step size (fundamental sample time)**`1/Fs`

Because none of the blocks in your model have a continuous sample time, a discrete solver is appropriate. For more information, see Solver Pane (Simulink).

Click

**OK**to close the dialog box.Save and close your model.

When you reopen and simulate the model, you see these results in the scope:

The top signal shows the fixed-point version of the sine wave input to the chart. The bottom signal corresponds to the filtered output from the chart. The filter removes high-frequency values from the signal but allows low-frequency values to pass through the chart unchanged.

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