Cast from Doubles to Fixed Point

This example shows you how to simulate a continuous real-world doubles signal using a generalized fixed-point data type. Using the fxpdemo_dbl2fix model, you can 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

To open the model, at the MATLAB^® command line, enter

openExample('fixedpoint/DoubleToFixedPointConversionExample')

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

Simulate Using Binary-Point-Only 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 set up the model to use binary-point-only scaling:

Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval [-5 5].
1. Double-click the Signal Generator block to open the Block Parameters dialog.
2. Set the Wave form parameter to sine.
3. Set the Amplitude parameter to 5.
4. Click OK.
Configure the Data Type Conversion (Dbl-to-FixPt) block.
1. Double-click the Dbl-to-FixPt block to open the Block Parameters dialog.
2. Verify that the Output data type parameter is fixdt(1,5,2). This 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, the minimum value is 100.00 = -4.00, and the precision is (1/2)² = 0.25.
3. Verify that the Integer rounding mode parameter is set to Floor. This rounds the fixed-point result toward negative infinity.
4. Select the Saturate on integer overflow check box to prevent the block from wrapping on overflow.
5. Click OK.
To simulate the model, in the Simulation tab, click Run.

The Scope displays the ideal and the 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.

To span the complete range of the input signal with 5 bits using binary-point-only scaling, set the output scaling to 2^-1. This puts the binary point one place to the left of the rightmost bit, giving a maximum value of 0111.1 = 7.5 and a minimum value of 1000.0 = -8.0. However, the precision is reduced to (1/2)¹ = 0.5. 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 see the effect of reducing the precision to 0.5, set the Output data type parameter of the Dbl-to-FixPt Data Type Conversion block to fixdt(1,5,1) and rerun the simulation.

Simulate Using [Slope Bias] Scaling

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 defined on the interval [-5 5].

To find the slope, you begin by assuming a fixed power-of-two exponent of -2. To find the fractional slope, 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 set up the model to use [Slope Bias] scaling:

Configure the Signal Generator block to output a sine wave signal with an amplitude defined on the interval [-5 5].
1. Double-click the Signal Generator block to open the Block Parameters dialog.
2. Set the Wave form parameter to sine.
3. Set the Amplitude parameter to 5.
4. Click OK.
Configure the Dbl-to-FixPt Data Type Conversion block.
1. Double-click the Dbl-to-FixPt block to open the Block Parameters dialog.
2. To specify a [Slope Bias] scaling of [0.3333 0], set the Output data type parameter to fixdt(1,5,0.3333,0).
3. Verify that the Integer rounding mode parameter is Floor. This rounds the fixed-point result toward negative infinity.
4. Select the Saturate on integer overflow check box to prevent the block from wrapping on overflow.
5. Click OK.
To simulate the model, in the Simulation tab, click Run.

The Scope displays the ideal and the fixed-point simulation results.

If you do not know the slope, you can achieve reasonable simulation results by selecting your scaling based on the formula

$\frac{(m a x_v a l u e - m i n_v a l u e)}{2^{w s} - 1},$

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.