Sine Wave

R2026b

Generate continuous or discrete sine wave

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Sine Wave block

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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.

When you set the Computation method parameter to Table lookup and the Optimize table for parameter to Speed, you can specify the frequency of the sine wave as any scalar or vector of scalars. The block generates a sine wave whose frequency is the closest achievable approximation using a table of length equal to the Maximum table length parameter. (since R2026b)

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, vector, or a matrix. 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 Tab

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

Optimize the table of sine values for one of the following:

• Speed –– The block precomputes a full table of sine values. The block supports arbitrary frequencies and sample rates. If the specified frequency is not exactly representable in the table, the block uses the closest representable frequency given the Maximum table length constraint. Use the read-only fields in the Info section to verify the frequency of the generated signal.

• Memory –– The table contains k/4 elements, where k = Fs/F. The period of each sinusoid must be an integer multiple of 4/Fs.

Dependencies

To enable this parameter, set:

• Sample mode to Discrete

• Computation method to Table lookup

Maximum table length — Maximum number of elements in the sine table

65535 (default) | positive integer

Specify the maximum number of elements in the sine table as a positive integer less than 10⁷. The block uses a lookup table with at most this many elements to represent the sine wave. Increasing this value allows the block to represent more frequencies exactly, at the cost of additional memory.

For vector frequencies, this limit applies individually to each frequency.

Dependencies

To enable this parameter, set:

• Sample mode to Discrete

• Computation method to Table lookup

• Optimize table for to Speed

Sample time — Sample period

1/1000 (default) | positive 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.

Info

Table length — Actual number of elements in the sine table

Read-only: 10 (default) | positive integer | vector

Since R2026b

This parameter is read-only.

Table length for the generated sine wave, displayed as a positive integer or a vector of length equal to the length of the Frequency (Hz) vector. Each element in the vector corresponds to the table length used for the respective frequency in the Frequency (Hz) parameter.

Dependencies

This field is visible when you set:

• Sample mode to Discrete

• Computation method to Table lookup

• Optimize table for to Speed

Actual frequency — Actual frequency of generated sine wave

Read-only: 10 (default) | scalar | vector

Since R2026b

This parameter is read-only.

Actual frequency of the generated sine wave in Hz, displayed as a scalar or a vector of length equal to the length of the Frequency (Hz) vector. This is the closest representable frequency to the value you specify in the Frequency (Hz) parameter, given the Maximum table length constraint. The block wraps this value to the range [0, Fs).

Dependencies

This field is visible when you set:

• Sample mode to Discrete

• Computation method to Table lookup

• Optimize table for to Speed

Frequency error — Difference between actual frequency and target frequency

Read-only: 0 (default) | scalar | vector

Since R2026b

This parameter is read-only.

Difference between the actual generated frequency and the specified target frequency in Hz, displayed as a scalar or a vector of length equal to the length of the Frequency (Hz) vector. A value of 0 indicates that the specified target frequency is exactly representable in the table.

Dependencies

This field is visible when you set:

• Sample mode to Discrete

• Computation method to Table lookup

• Optimize table for to Speed

Data Types Tab

Output data type — Output data type

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

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

• Inherit:Inherit via back propagation — Inherit via the 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).

Block Characteristics

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

More About

Sinusoid

A real-valued, discrete-time sinusoid is defined as:

$$y(n)=A\sin (2\pi fn+\varphi )$$

where A is the amplitude, f is the frequency in Hz, and φ is the initial phase, or phase offset, in radians.

A complex sinusoid is defined as:

$$y(n)=A{e}^{j(2\pi fn+\varphi )}$$

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 unique samples of every output sinusoid at the start of simulation, and recalls the samples from memory as needed. A table of finite length can only be constructed when all output sequences repeat.

When you set the Optimize table for parameter to Speed, the block precomputes a full table of sine values and recalls the samples from memory as needed. The block supports arbitrary frequencies and sample rates. If the frequency you specify is not exactly representable in the table, the block uses the closest representable frequency given the constraint of the Maximum table length parameter value. To determine the actual frequency of the generated sine wave, use the read-only fields, Actual frequency and Frequency error in the Info section of the block dialog box.

When you set the Optimize table for parameter to Memory, the block constructs a lookup table with k/4 elements for each channel, where k = Fs/F. Here, Fs = 1/Ts, Ts is the value of the Sample time parameter, and F is the frequency specified in the Frequency (Hz) parameter.

For long output sequences, the table lookup method requires far fewer floating-point operations than any of the other methods, but it 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 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™.

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

HDL Architecture

This block has one default HDL architecture.

HDL Block Properties

ConstrainedOutputPipeline	Number of registers to place at the outputs by moving existing delays in the design. Distributed pipelining does not redistribute these registers. The default value 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 value 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 value is 0. For more details, see OutputPipeline (HDL Coder).
SynthesisAttributes	Specifies the synthesis attributes for the blocks and block output signals in the model. The generated HDL code contains these attributes. For more information, see SynthesisAttributes (HDL Coder).

Data Type Support

The block supports these data types for HDL code generation:

Output Port	Dimension	Fixed-Point	Floating-Point	Built-in Integers	Bus	Boolean	Complex Signal
Port_1	Scalar Vector Matrix	Yes	Single Double	Yes	Yes	Yes	Yes

When you use Output data type as single or double for the block, you can generate synthesizable HDL code by using native floating-point technology. For more information, see Generate Target-Independent HDL Code with Native Floating-Point (HDL Coder). (since R2026a)

Block Parameter Configuration

Block Parameter	Limitations
Computation method	Computation method must be set to Table lookup.
Sample mode	Sample mode must be set to Discrete.

Optimizations

The block participates in these HDL optimizations to optimize the speed, and area.

Speed Optimization

Optimization	Description
Specify Distributed Pipelining Settings (HDL Coder)	Distributed pipelining, or register retiming, is a speed optimization that moves existing delays in a design to reduce the critical path while preserving functional behavior.
Clock-Rate Pipelining (HDL Coder)	Clock-rate pipelining is an optimization framework in HDL Coder that allows other speed and area optimizations to introduce latency at the clock rate.
Delay Balancing (HDL Coder)	Using delay balancing, HDL Coder detects introduced latency along one path and then inserts matching delays on the other paths in your generated model.
Critical Path Estimation (HDL Coder)	To quickly identify the most likely critical path in your design, use Critical Path Estimation. Critical path estimation speeds up the iterative process of finding the critical path. To know blocks that are characterized in critical path estimation, see Characterized Blocks (HDL Coder).

Restrictions

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

Version History

Introduced before R2006a

R2026b: Support for arbitrary frequencies in table lookup mode

When you set the Computation method parameter to Table lookup and the Optimize table for parameter to Speed, you can specify any scalar or vector of scalars for the Frequency (Hz) parameter and any positive scalar for the Sample time parameter.

If the frequency you specify is not exactly representable in the table, the block uses the closest achievable approximation based on a lookup table of length equal to Maximum table length. Use the read-only Actual frequency and Frequency error parameters to verify the generated frequency.

These new parameters and fields support this feature:

• Maximum table length — Maximum number of elements in the precomputed sine table.

• Table length — Read-only field that displays the actual table length.

• Actual frequency — Read-only field that displays the actual frequency of the generated sine wave.

• Frequency error — Read-only field that displays the difference between the actual frequency and the specified frequency.

Existing models that use table lookup mode continue to produce numerically identical results when the default maximum table length remains unchanged.

When exporting Simulink models to releases R2026a and earlier, the Sine Wave block uses the Table lookup mode if the generated frequency is exactly representable within the legacy table-length limit. Otherwise, the block switches to the Differential mode to preserve the functional behavior. This mode can introduce small accumulated numerical error over long simulations.

R2026a: Use HDL optimizations and native floating-point

When you use Output data type as single or double for the Sine Wave block, you can generate synthesizable HDL code by using native floating-point technology. To generate the HDL code with native floating-point, in the HDL Code Generation > Floating-Point pane of the Configuration Parameters dialog box, select the Use floating-point parameter. For more information on native floating-point, see Generate Target-Independent HDL Code with Native Floating-Point (HDL Coder).

You can also use various HDL optimizations, such as distributed pipelining, hierarchy flattening, or balancing, for the block to generate optimized HDL code for your DSP application.

R2026a: Improvements in Sine Wave block

When you set Computation method to Table lookup and Optimize table for to Speed, the Sine Wave block supports frequency, F, and the sample rate Fs, values such that F/Fs can be represented as a ratio of 16 bit integers. For example, if you set F as 1.35 Hz and Fs as 2.15 Hz, the ratio of F/Fs can be written as 27/43, which can be represented by 16-bit integers.

When you set Computation method to Trigonometric fcn, the Sine Wave block has been improved with phase calculations for greater numerical accuracy and consistency. As a result, the output values can differ from previous releases, especially for long signals.