The purpose of this example is to show you how to simulate a continuous real-world doubles signal using a generalized fixed-point data type. Although simple in design, the model gives you an opportunity to explore many of the important features of the Fixed-Point Designer™ software, including

Data types

Scaling

Rounding

Logging minimum and maximum simulation values to the workspace

Overflow handling

This example uses the `fxpdemo_dbl2fix`

model.
Open the model:

fxpdemo_dbl2fix

The sections that follow describe the model and its simulation results.

In this example, you configure the Signal
Generator block to output a sine wave signal with an amplitude
defined on the interval `[-5 5]`

. The Signal
Generator block always outputs double-precision numbers.

The Data Type Conversion (Dbl-to-FixPt) block converts the double-precision numbers from the Signal Generator block into one of the Fixed-Point Designer data types. For simplicity, the size of the output signal is 5 bits in this example.

The Data Type Conversion (FixPt-to-Dbl)
block converts one of the Fixed-Point
Designer data types into
a Simulink^{®} data type. In this example, it outputs double-precision
numbers.

The following sections describe how to simulate the model using binary-point-only scaling and [Slope Bias] scaling.

When using binary-point-only scaling, your goal is to find the
optimal power-of-two exponent *E*, as defined in Scaling. For this scaling mode, the fractional
slope *F* is 1 and there is no bias.

To run the simulation:

Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval

`[-5 5]`

.Double-click the Signal Generator block to open the

`Block Parameters`

dialog.Set the

**Wave form**parameter to`sine`

.Set the

**Amplitude**parameter to`5`

.Click

**OK**.

Configure the Data Type Conversion (Dbl-to-FixPt) block.

Double-click the

**Dbl-to-FixPt**block to open the`Block Parameters`

dialog.Verify that the

**Output data type**parameter is`fixdt(1,5,2)`

.`fixdt(1,5,2)`

specifies a 5-bit, signed, fixed-point number with scaling`2^-2`

, which puts the binary point two places to the left of the rightmost bit. Hence the maximum value is 011.11 = 3.75, a minimum value of 100.00 = -4.00, and the precision is (1/2)^{2}= 0.25.Verify that the

**Integer rounding mode**parameter is`Floor`

.`Floor`

rounds the fixed-point result toward negative infinity.Select the

**Saturate on integer overflow**checkbox to prevent the block from wrapping on overflow.Click

**OK**.

Select

**Simulation**>**Run**in your Simulink model window.

The Scope displays the real-world and fixed-point simulation results.

The simulation shows the quantization effects
of fixed-point arithmetic. Using a 5-bit word with a precision of (1/2)^{2} = 0.25
produces a discretized output that does not span the full range of
the input signal.

If you want to span the complete range of the input signal with
5 bits using binary-point-only scaling, then your only option is to
sacrifice precision. Hence, the output scaling is `2^-1`

,
which puts the binary point one place to the left of the rightmost
bit. This scaling gives a maximum value of 0111.1 = 7.5, a minimum
value of 1000.0 = -8.0, and a precision of (1/2)^{1} =
0.5.

To simulate using a precision of 0.5, set the **Output
data type** parameter of the Data
Type Conversion (Dbl-to-FixPt) block to `fixdt(1,5,1)`

and
rerun the simulation.

When using [Slope Bias] scaling, your goal is to find the optimal
fractional slope *F* and fixed power-of-two exponent *E*,
as defined in Scaling. There is no
bias for this example because the sine wave is on the interval ```
[-5
5]
```

.

To arrive at a value for the slope, you begin by assuming a
fixed power-of-two exponent of -2. To find the fractional slope, you
divide the maximum value of the sine wave by the maximum value of
the scaled 5-bit number. The result is 5.00/3.75 = 1.3333. The slope
(and precision) is 1.3333.(0.25) = 0.3333. You specify the [Slope
Bias] scaling as [0.3333 0] by entering the expression `fixdt(1,5,0.3333,0)`

as
the value of the **Output data type** parameter.

You could also specify a fixed power-of-two exponent of -1 and
a corresponding fractional slope of 0.6667. The resulting slope is
the same since *E* is reduced by 1 bit but *F* is
increased by 1 bit. The Fixed-Point
Designer software would automatically
store *F* as 1.3332 and *E* as
-2 because of the normalization condition of 1
≤ *F* < 2.

To run the simulation:

Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval

`[-5 5]`

.Double-click the Signal Generator block to open the

`Block Parameters`

dialog.Set the

**Wave form**parameter to`sine`

.Set the

**Amplitude**parameter to`5`

.Click

**OK**.

Configure the Data Type Conversion (Dbl-to-FixPt) block.

Double-click the

**Dbl-to-FixPt**block to open the`Block Parameters`

dialog.Set the

**Output data type**parameter to`fixdt(1,5,0.3333,0)`

to specify [Slope Bias] scaling as [0.3333 0].Verify that the

**Integer rounding mode**parameter is`Floor`

.`Floor`

rounds the fixed-point result toward negative infinity.Select the

**Saturate on integer overflow**checkbox to prevent the block from wrapping on overflow.Click

**OK**.

Select

**Simulation**>**Run**in your Simulink model window.

The Scope displays the real-world and fixed-point simulation results.

You do not need to find the slope using this method. You need only the range of the data you are simulating and the size of the fixed-point word used in the simulation. You can achieve reasonable simulation results by selecting your scaling based on the formula

$$\frac{\left(max\_value-min\_value\right)}{{2}^{ws}-1},$$

where

*max_value*is the maximum value to be simulated.*min_value*is the minimum value to be simulated.*ws*is the word size in bits.2

^{ws}- 1 is the largest value of a word with size*ws*.

For this example, the formula produces a slope of 0.32258.

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