Sine Wave

Generate continuous or discrete sine wave

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Libraries:
DSP System Toolbox / Sources
DSP System Toolbox HDL Support / Sources

Description

The Sine Wave block generates a multichannel real or complex sinusoidal signal, with independent amplitude, frequency, and phase in each output channel. The block supports floating point and signed fixed-point data types.

The block generates a real sinusoidal signal when you set the Output complexity parameter to Real. The real sinusoidal output is defined by an expression of the type

$$y=A\sin \left(2\pi ft+\varphi \right)$$

where you specify A in the Amplitude parameter, f in hertz in the Frequency parameter, and ϕ in radians in the Phase offset parameter.

The block generates a complex exponential signal when you set the Output complexity parameter to Complex. This complex exponential signal is defined by an expression of the type

$$y=A{e}^{j(2\pi ft+\varphi )}=A\left\{\cos \left(2\pi ft+\varphi \right)+j\sin \left(2\pi ft+\varphi \right)\right\}$$

Generating Multichannel Outputs

For both real and complex sinusoids, the Amplitude, Frequency, and Phase offset parameter values (A, f, and ϕ) can be scalars or length-N vectors, where N is the desired number of channels in the output. When you specify at least one of these parameters as a length-N vector, scalar values specified for the other parameters are applied to every channel.

For example, to generate the three-channel output containing the following real sinusoids, set the block parameters as shown:

$$y=\{\begin{array}{cc}\sin \left(2000\pi t\right)& \text{ (channel 1)}\\ 2\sin \left(1000\pi t\right)& \text{ (channel 2)}\\ 3\sin \left(500\pi t+\frac{\pi }{2}\right)& \text{ (channel 3)}\end{array}$$

• Output complexity = Real

• Amplitude = [1 2 3]

• Frequency = [1000 500 250]

• Phase offset = [0 0 pi/2]

Examples

Generate Sample-Based Sine Waves

This example compares the different methods of generating sample-based sine waves from the Sine Wave block in DSP System Toolbox.

Generate Frame-Based Sine Waves

This example compares the different methods of generating frame-based sine waves from the Sine Wave block in DSP System Toolbox™.

Ports

Output

Port_1 — Sinusoidal signal

scalar | vector | matrix

Output a sinusoidal signal as a scalar or vector. For more information about output complexity, see Description. For information about multichannel support, see Generating Multichannel Outputs.

Tip

To output fixed-point data types, you must set Sample mode to Discrete and Computation method to Table lookup.

Data Types: single | double | fixed point
Complex Number Support: Yes

Parameters

Main

Amplitude — Amplitude of sine waves

1 (default) | scalar | vector

A length-N vector containing the amplitudes of the sine waves in each of N output channels, or a scalar to be applied to all N channels. The vector length must be the same as that specified for the Frequency and Phase offset parameters.

Tip

This parameter is tunable (Simulink) only when the Computation method is Trigonometric fcn or Differential.

Tunable: Yes

Frequency (Hz) — Frequency of each sine wave

100 (default) | scalar | vector

A length-N vector containing frequencies, in hertz, of the sine waves in each of N output channels, or a scalar to be applied to all N channels. The vector length must be the same as that specified for the Amplitude and Phase offset parameters. You can specify positive, zero, or negative frequencies.

Tip

This parameter is tunable (Simulink) when you set:

• Solver Type to Fixed-step.

• Sample mode to Continuous.

• Sample mode to Discrete and Computation method to Trigonometric fcn.

Tunable: Yes

Phase offset (rad) — Phase offset

0 (default) | scalar | vector

A length-N vector containing the phase offsets, in radians, of the sine waves in each of N output channels, or a scalar to be applied to all N channels. The vector length must be the same as that specified for the Amplitude and Frequency parameters.

Tip

This parameter is tunable (Simulink) when you set:

• Solver Type to Fixed-step.

• Sample mode to Continuous.

• Sample mode to Discrete and Computation method to Trigonometric fcn.

Tunable: Yes

Sample mode — Continuous or discrete sampling mode

Discrete (default) | Continuous

Specify the sampling mode as Continuous or Discrete:

• Continuous

  In continuous mode, the sinusoid in the ith channel, y_i, is computed as a continuous function,

  $$\begin{array}{ll}{y}_i=A_i\sin \left(2\pi f_{i}t+{\varphi }_i\right)\hfill & \text{(real)}\hfill \\ \begin{array}{l}\\ \text{or}\\ \end{array}\hfill & \hfill \\ y_i=A_i{e}^{j\left(2\pi f_{i}t+{\varphi }_i\right)}\hfill & \text{(complex)}\hfill \end{array}$$

  and the block's output is continuous. In this mode, the block operates the same as the Simulink^® Sine Wave block with Sample time set to 0. This mode offers high accuracy, but requires trigonometric function evaluations at each simulation step, which is computationally expensive. Also, because this method tracks absolute simulation time, a discontinuity will eventually occur when the time value reaches its maximum limit.

  Note also that many DSP System Toolbox™ blocks do not accept continuous-time inputs.

• Discrete

  In discrete mode, the block can generate discrete-time output by directly evaluating the trigonometric function, by table lookup, or by a differential method. For more information on these computation methods, see Algorithms.

Output complexity — Real or complex waveform

Real (default) | Complex

The type of waveform to generate: Real specifies a real sine wave, Complex specifies a complex exponential.

Computation method — Method for computing discrete-time sinusoids

Trigonometric fcn (default) | Table lookup | Differential

The method by which discrete-time sinusoids are generated: Trigonometric fcn, Table lookup, or Differential. For more information on each of the available options, see Algorithms.

Dependencies

This parameter is only visible when you set the Sample mode to Discrete.

Note

To generate fixed-point sinusoids, you must set the Computation method to Table lookup.

Optimize table for — Optimize for speed or memory

Speed (default) | Memory

Optimizes the table of sine values for Speed or Memory. When optimized for speed, the table contains k elements, and when optimized for memory, the table contains k/4 elements, where k is the number of input samples in one full period of the sine wave.

Dependencies

This parameter is only visible when you set the Computation method parameter to Table lookup.

Sample time — Sample period

1/1000 (default) | scalar

The period with which the sine wave is sampled, T_s, as a finite scalar, greater than zero. The output frame period of the block is MT_s, where you specify M in the Samples per frame parameter.

Dependencies

To enable this parameter, set Sample mode to Discrete.

Samples per frame — Samples per frame

1 (default) | positive integer

The number of consecutive samples from each sinusoid to buffer into the output frame, M, specified as a positive scalar integer. This parameter is not tunable.

The block output is an M-by-N matrix with frame period MT_s, where you specify T_s in the Sample time parameter.

Dependencies

To enable this parameter, set Sample mode to Discrete.

Resetting states when re-enabled — State behavior inside enabled subsystems

Restart at time zero (default) | Catch up to simulation time

This parameter determines the behavior of the Sine Wave block when an enabled subsystem is reenabled. The block can either reset itself to its starting state (Restart at time zero), or resume generating the sinusoid based on the current simulation time (Catch up to simulation time).

Dependencies

This parameter only applies when the Sine Wave block is located inside an enabled subsystem and the States when enabling parameter of the Enable (Simulink) block is set to reset.

Data Types

Output data type — Output data type

double (default) | single | fixdt(1,16) | fixdt(1,16,0) | <data type expression> | Inherit:Inherit via back propagation

Select how you would like to specify the data type properties of the Output data type. You can choose:

• Inherit — Lets you specify a rule for inheriting a data type, for example, Inherit: Inherit via back propagation

• Built in— Lets you specify a built in data type, for example, double

• Fixed point — Lets you specify the fixed-point attributes of the data type.

• Expression — Lets you specify an expression that evaluates to a valid data type, for example, fixdt(1,16)

Data Type Assistant

Mode — Data type mode

Built in (default) | Inherit | Fixed point | Expression

Select how you would like to specify the data type properties of the Output data type. You can choose:

• Inherit — Lets you specify a rule for inheriting a data type, for example, Inherit: Inherit via back propagation

• Built in— Lets you specify a built-in data type, for example, double

• Fixed point — Lets you specify the fixed-point attributes of the data type.

• Expression — Lets you specify an expression that evaluates to a valid data type, for example, fixdt(1,16)

For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Signedness — Signedness of fixed-point data

Signed (default)

Specify the signedness of the fixed-point output. For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Limitations

The Sine Wave only supports Signed data types.

Scaling — Method for scaling fixed-point data

Best precision (default) | Binary point

Specify the method for scaling your fixed-point data to avoid overflow conditions and minimize quantization errors. For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Dependencies

To enable this parameter, set Mode to Fixed point

Word length — Bit size of the word that holds the quantized integer

16 (default) | integer from 2 to 128

Specify the bit size of the word that holds the quantized integer as a positive integer from 2 to 128. For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Dependencies

To enable this parameter, set Mode to Fixed point

Fraction length — Fraction length for fixed-point data type

0 (default) | integer scalar

Specify the fraction length of the fixed-point data type as a positive or negative integer scalar.

Dependencies

To enable this parameter, set Mode to Fixed point and Scaling to Binary point.

Data type override — Data type override mode

Inherit (default) | Off

Select the data type override mode for this signal. You can select:

• Inherit — Inherits the data type override setting specified for the model.

• Off — Ignores the data type override setting specified for the model and uses the fixed-point data type you specify.

Dependencies

To enable this parameter, set Mode to Built in or Fixed point. For more information, see Specify Data Types Using Data Type Assistant (Simulink).

Block Characteristics

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

Algorithms

When you select Discrete from the Sample mode parameter, the secondary Computation method parameter provides three options for generating the discrete sinusoid: Trigonometric fcn, Table lookup, and Differential.

Trigonometric Fcn

The trigonometric function method computes the sinusoid in the ith channel, y_i, by sampling the continuous function

$$\begin{array}{ll}{y}_i=A_i\sin \left(2\pi f_{i}t+{\varphi }_i\right)\hfill & \text{(real)}\hfill \\ \begin{array}{l}\\ \text{or}\\ \end{array}\hfill & \hfill \\ y_i=A_i{e}^{j\left(2\pi f_{i}t+{\varphi }_i\right)}\hfill & \text{(complex)}\hfill \end{array}$$

with a period of T_s, where you specify T_s in the Sample time parameter. This mode of operation has the same benefits and liabilities as the Continuous sample mode.

At each sample time, the block evaluates the sine function at the appropriate time value within the first cycle of the sinusoid. By constraining trigonometric evaluations to the first cycle of each sinusoid, the block avoids the imprecision of computing the sine of very large numbers, and eliminates the possibility of discontinuity during extended operations (when an absolute time variable might overflow). This method therefore avoids the memory demands of the table lookup method at the expense of many more floating-point operations.

Table Lookup

The table lookup method precomputes the unique samples of every output sinusoid at the start of the simulation, and recalls the samples from memory as needed. Because a table of finite length can only be constructed when all output sequences repeat, the method requires that the period of every sinusoid in the output be evenly divisible by the sample period. That is, 1/(f_iT_s) = k_i must be an integer value for every channel i = 1, 2, ..., N.

When the Optimize table for parameter is set to Speed, the table constructed for each channel contains k_i elements. When the Optimize table for parameter is set to Memory, the table constructed for each channel contains k_i/4 elements.

For long output sequences, the table lookup method requires far fewer floating-point operations than any of the other methods, but can demand considerably more memory, especially for high sample rates (long tables). This method is recommended for models that are intended to emulate or generate code for DSP hardware, and that therefore must be optimized for execution speed.

Note

The lookup table for this block is constructed from double-precision floating-point values. Thus, when you use the Table lookup computation mode, the maximum amount of precision you can achieve in your output is 53 bits. Setting the word length of the Output or User-defined data type to values greater than 53 bits does not improve the precision of your output.

Tip

To generate fixed-point sinusoids, you must select Table Lookup.

Differential

The differential method uses an incremental algorithm. This algorithm computes the output samples based on the output values computed at the previous sample time (and precomputed update terms) by using the following identities.

$$\begin{array}{l}\sin \left(t+T_s\right)=\sin \left(t\right)\cos \left(T_s\right)+\cos \left(t\right)\sin \left(T_s\right)\\ \cos \left(t+T_s\right)=\cos \left(t\right)\cos \left(T_s\right)-\sin \left(t\right)\sin \left(T_s\right)\end{array}$$

The update equations for the sinusoid in the ith channel, y_i, can therefore be written in matrix form as

$$\left[\begin{array}{c}\sin \left\{2\pi f_i\left(t+T_s\right)+{\varphi }_i\right\}\\ \cos \left\{2\pi f_i\left(t+T_s\right)+{\varphi }_i\right\}\end{array}\right]=\left[\begin{array}{cc}\cos \left(2\pi f_i{T}_s\right)& \sin \left(2\pi f_i{T}_s\right)\\ -\sin \left(2\pi f_i{T}_s\right)& \cos \left(2\pi f_i{T}_s\right)\end{array}\right]\left[\begin{array}{c}\sin \left(2\pi f_{i}t+{\varphi }_i\right)\\ \cos \left(2\pi f_{i}t+{\varphi }_i\right)\end{array}\right]$$

where you specify T_s in the Sample time parameter. Since T_s is constant, the right-hand matrix is a constant and can be computed once at the start of the simulation. The value of A_isin[2πf_i(t+T_s)+ϕ_i] is then computed from the values of sin(2πf_it+ϕ_i) and cos(2πf_it+ϕ_i) by a simple matrix multiplication at each time step.

This mode offers reduced computational load, but is subject to drift over time due to cumulative quantization error. Because the method is not contingent on an absolute time value, there is no danger of discontinuity during extended operations (when an absolute time variable might overflow).

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using Simulink® Coder™.

The Sine Wave block references absolute simulation time when configured in continuous sample mode.

HDL Code Generation

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

Note

For a sine wave generator that is optimized for HDL code generation and has hardware-friendly control signals, see NCO (DSP HDL Toolbox), and Generate Sine Wave (DSP HDL Toolbox). The DSP HDL Toolbox™ blocks provide HDL-optimized algorithms with hardware-friendly control signals and simulate the latency of the HDL algorithm in Simulink.

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

HDL Architecture

This block has one default HDL architecture.

Restrictions

For HDL code generation, you must select the following Sine Wave block settings:

• Computation method: Table lookup

• Sample mode: Discrete

Output:

• The output port cannot have data types single or double.

• This block does not support frame-based vector output during HDL code generation. The vector outputs from amplitude and frequency array are supported.

Complex Data Support

This block supports code generation for complex signals.

Version History

Introduced before R2006a