Sine, Cosine

Implement fixed-point sine or cosine wave using lookup table approach that exploits quarter wave symmetry

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Libraries:
Simulink / Lookup Tables

Description

The Sine and Cosine block implements a sine and/or cosine wave in fixed point using a lookup table method that exploits quarter wave symmetry. The block can output the following functions of the input signal, depending upon what you select for the Output formula parameter:

• sin(2πu)

• cos(2πu)

• exp(j2πu)

• sin(2πu) and cos(2πu)

You define the number of lookup table points in the Number of data points for lookup table parameter. The block implementation is most efficient when you specify the lookup table data points to be (2^n)+1, where n is an integer.

Use the Output word length parameter to specify the word length of the fixed-point output data type. The fraction length of the output is the output word length minus 2.

Examples

Digital Waveform Generation: Approximate a Sine Wave

Design and evaluate a sine wave data table for use in digital waveform synthesis applications in embedded systems and arbitrary waveform generation instruments.

Open Model

Ports

Input

u — Input signal to implement as fixed-point sine or cosine wave

real-valued signal

Input signal, u, specified as a real-valued scalar, vector, or matrix.

Tip

To obtain meaningful block output, the block input values should fall within the range [0, 1). For input values that fall outside this range, the values are cast to an unsigned data type, where overflows wrap. For these out-of-range inputs, the block output might not be meaningful.

Data Types: single | double | int8 | int16 | int32 | int64 | uint8 | uint16 | uint32 | uint64 | Boolean | fixed point

Output

sin(2*pi*u) — Fixed-point sine wave

real-valued fixed-point signal

Fixed-point sine wave, implemented using a lookup table approach.

Dependencies

This port is enabled when the Output formula is set to sin(2*pi*u) or sin(2*pi*u) and cos(2*pi*u).

Data Types: fixed point

cos(2*pi*u) — Fixed-point cosine wave

real-valued fixed-point signal

Fixed-point cosine wave, implemented using a lookup table approach.

Dependencies

This port is enabled when the Output formula is set to cos(2*pi*u) or sin(2*pi*u) and cos(2*pi*u).

Data Types: fixed point

exp(j*2*pi*u) — exp(j*2*pi*u)

complex-valued fixed-point signal

exp(j*2*pi*u), implemented using a lookup table approach.

Dependencies

This port is enabled when the Output formula is set to exp(j*2*pi*u).

Data Types: fixed point

Parameters

Output formula — Select the signal(s) to output

cos(2*pi*u) | sin(2*pi*u) | exp(j*2*pi*u) | sin(2*pi*u) and cos(2*pi*u)

Programmatic Use

Block Parameter: Formula

Values: 'sin(2*pi*u)' | 'cos(2*pi*u)' | 'exp(j*2*pi*u)' | 'sin(2*pi*u) and cos(2*pi*u)'

Number of data points for lookup table — Specify the number of data points to retrieve from the lookup table

(2^5)+1 (default) | integer, greater than or equal to 2

The implementation is most efficient when you specify the lookup table data points to be (2^n)+1, where n is an integer. To be compatible with the Output word length parameter, the Number of data points for lookup table must be less than or equal to (2^(Output word length-2)+1).

Programmatic Use

Block Parameter: NumDataPoints

Type: scalar

Value: integer >= 2

Default: '(2^5)+1'

Output word length — Specify the word length for the fixed-point data type of the output signal

16 (default) | integer from 2 to 53

The fraction length of the output is the output word length minus 2. To be compatible with the Number of data points for lookup table parameter, (2^(Output word length - 2) +1) must be greater than or equal to Number of data points for lookup table.

Note

The block uses double-precision floating-point values to construct lookup tables. Therefore, the maximum amount of precision you can achieve in your output is 53 bits. Setting the word length to values greater than 53 bits does not improve the precision of your output.

Programmatic Use

Block Parameter: OutputWordLength

Type: scalar

Value: integer from 2 to 53

Default: '16'

Internal rule priority for lookup table — Specify the internal rule for intermediate calculations

Speed (default) | Precision

Select Speed for faster calculations. If you do, a loss of accuracy might occur, usually up to 2 bits.

Programmatic Use

Block Parameter: InternalRulePriority

Values: 'Speed' | 'Precision'

Default: 'Speed'

Block Characteristics

Data Types	Boolean | double | fixed point | integer | single
Direct Feedthrough	no
Multidimensional Signals	no
Variable-Size Signals	no
Zero-Crossing Detection	no

Extended Capabilities

C/C++ Code Generation
Generate C and C++ code using Simulink® Coder™.

HDL Code Generation

Generate VHDL, Verilog and SystemVerilog code for FPGA and ASIC designs using HDL Coder™.

HDL Coder™ provides additional configuration options that affect HDL implementation and synthesized logic.

HDL Architecture

The HDL code implements Cosine and Sine blocks by using the quarter-wave lookup table that you specify in the Simulink block parameters.

To avoid generating a division operator (/) in the HDL code, for Number of data points for lookup table, enter (2^n)+1. n is an integer.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default is 0. For more details, see ConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in the generated code. Distributed pipelining and constrained output pipelining can move these registers. The default is 0. For more details, see OutputPipeline (HDL Coder).

Limitations

If you use Intel^® MAX 10 device, to map the lookup table to RAM, add this Tcl command when creating the project in the Quartus tool:

set_global_assignment -name INTERNAL_FLASH_UPDATE_MODE "SINGLE IMAGE WITH ERAM"

Fixed-Point Conversion
Design and simulate fixed-point systems using Fixed-Point Designer™.

Version History

Introduced before R2006a