| Simulink® Fixed Point™ | |
| On this page… |
|---|
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 Simulink® Fixed Point™ software, including
Data types
Scaling
Rounding
Logging minimum and maximum simulation values to the workspace
Overflow handling
The model used in this example is given by the fxpdemo_dbl2fix demo. You can launch this demo by typing its name at the MATLAB® command line:
fxpdemo_dbl2fix
The model is shown in the following figure.
The sections that follow describe the model and its simulation results.
For purposes of this documentation example, the Signal Generator block is configured to output a sine wave signal with an amplitude defined on the interval [-5 5]. It always outputs double-precision numbers.
The function of the Data Type Conversion (Dbl-to-FixPt) block is to convert the double-precision numbers from the Signal Generator block into one of the Simulink Fixed Point data types. For simplicity, its output signal is limited to 5 bits in this example.
The function of the Data Type Conversion (FixPt-to-Dbl) block is to convert one of the Simulink Fixed Point data types into a Simulink® data type. In this example, it outputs double-precision numbers.
The results of two simulation trials are given below. The first trial uses binary-point-only scaling while the second trial uses [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 set to 1 and no bias is required.
The Data Type Conversion (Dbl-to-FixPt) block is configured in this way:
Output data type and scaling
The output data type is given by 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. This gives a maximum value of 011.11 = 3.75, a minimum value of 100.00 = -4.00, and a precision of (1/2)2 = 0.25.
Rounding
The rounding mode is given by Floor. This rounds the fixed-point result toward negative infinity.
Overflows
Fixed-point values that overflow wrap to the appropriate value that is representable by the data type.
The resulting real-world and fixed-point simulation results are shown in the following figure.
The simulation clearly demonstrates the quantization effects of fixed-point arithmetic. The combination of 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 would be given by 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.
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. No bias is required for this example because the sine wave is defined on the interval [-5 5]. The Data Type Conversion (Dbl-to-FixPt) block configuration is the same as that of the previous trial except for the scaling.
To arrive at a value for the slope, you can begin by assuming a fixed power-of-two exponent of -2. In the previous trial, this value defined the binary-point-only scaling and resulted in a precision of 0.25. 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.
Of course, you could have specified a fixed power-of-two exponent of -1 and a corresponding fractional slope of 0.6667. Naturally, the resulting slope is the same since E was reduced by one bit but F was increased by one bit. In this case, the blockset would automatically store F as 1.3332 and E as -2 because of the normalization condition of 1 ≤ F < 2.
The resulting real-world and fixed-point simulation results are shown in the following figure.
This somewhat cumbersome process used to find the slope is not really necessary. All that is required is the range of the data you are simulating and the size of the fixed-point word used in the simulation. In general, you can achieve reasonable simulation results by selecting your scaling based on the formula
where
max is the maximum value to be simulated.
min is the minimum value to be simulated.
ws is the word size in bits.
2ws - 1 is the largest value of a word with size ws.
For this example, the formula produces a slope of 0.32258.
| Simulink® Fixed Point™ Software Features | Examples | |
| © 1984-2008- The MathWorks, Inc. - Site Help - Patents - Trademarks - Privacy Policy - Preventing Piracy - RSS |