Sine Wave

Generate continuous or discrete sine wave

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

Description

TheSine Waveblock 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 theOutput complexityparameter toReal. The real sinusoidal output is defined by an expression of the type

$y = A \sin (2 π f t + ϕ)$

你指定Ain theAmplitudeparameter,fin hertz in theFrequencyparameter, andϕin radians in thePhase offsetparameter.

The block generates a complex exponential signal when you set theOutput complexityparameter toComplex. This complex exponential signal is defined by an expression of the type

$y = A e^{j (2 π f t + ϕ)} = A {\cos (2 π f t + ϕ) + j \sin (2 π f t + ϕ)}$

Generating Multichannel Outputs

For both real and complex sinusoids, theAmplitude,Frequency, andPhase offsetparameter values (A,f, andϕ) can be scalars or length-Nvectors, whereNis the desired number of channels in the output. When you specify at least one of these parameters as a length-Nvector, 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:

$y = {\begin{matrix} \sin (2000 π t) & (channel 1) \\ 2 \sin (1000 π t) & (channel 2) \\ 3 \sin (500 π t + \frac{π}{2}) & (channel 3) \end{matrix}$

Output complexity=Real
Amplitude=[1 2 3]
Frequency=[1000 500 250]
Phase offset=[0 0 pi/2]

Examples

Generate Frame-Based Sine Waves

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

Open Model

Generate Sample-Based Sine Waves

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

Open Model

Ports

Output

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Port_1—Sinusoidal signal
scalar | vector | matrix

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

Tip

To output fixed-point data types, you must setSample modetoDiscreteandComputation methodtoTable lookup.

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

Parameters

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Main

Amplitude—Amplitude of sine waves
`1`(default) | scalar | vector

A length-Nvector containing the amplitudes of the sine waves in each ofN输出通道,或a scalar to be applied to allNchannels. The vector length must be the same as that specified for theFrequencyandPhase offsetparameters.

Tip

This parameter istunable(Simulink)only when theComputation methodisTrigonometric fcnorDifferential.

Tunable:Yes

Frequency (Hz)—Frequency of each sine wave
`100`(default) | scalar | vector

A length-Nvector containing frequencies, in hertz, of the sine waves in each ofN输出通道,或a scalar to be applied to allNchannels. The vector length must be the same as that specified for theAmplitudeandPhase offsetparameters. You can specify positive, zero, or negative frequencies.

Tip

This parameter istunable(Simulink)when you set either:

Sample modetoContinuous.
Sample modetoDiscreteandComputation methodtoTrigonometric fcn.

Tunable:Yes

Phase offset (rad)—Phase offset
`0`(default) | scalar | vector

A length-Nvector containing the phase offsets, in radians, of the sine waves in each ofN输出通道,或a scalar to be applied to allNchannels. The vector length must be the same as that specified for theAmplitudeandFrequencyparameters.

Tip

This parameter istunable(Simulink)when you set either:

Sample modetoContinuous.
Sample modetoDiscreteandComputation methodtoTrigonometric fcn.

Tunable:Yes

Sample mode—Continuous or discrete sampling mode
`Discrete`(default) |`Continuous`

Specify the sampling mode asContinuousorDiscrete:

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

$\begin{array}{l} y_{i} = A_{i} \sin (2 π f_{i} t + ϕ_{i}) & (real) \\ \begin{array}{l} or \end{array} \\ y_{i} = A_{i} e^{j (2 π f_{i} t + ϕ_{i})} & (complex) \end{array}$

and the block's output is continuous. In this mode, the block operates the same as the Simulink^®Sine Wave block withSample timeset to0. 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, seeAlgorithms.

Output complexity—Real or complex waveform
`Real`(default) |`Complex`

The type of waveform to generate:Realspecifies a real sine wave,Complexspecifies 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, orDifferential. For more information on each of the available options, seeAlgorithms.

Dependencies

This parameter is only visible when you set theSample modetoDiscrete.

Note

To generate fixed-point sinusoids, you must set theComputation methodtoTable lookup.

Optimize table for—优化速度或内存
`Speed`(default) |`Memory`

Optimizes the table of sine values forSpeedorMemory. When optimized for speed, the table containskelements, and when optimized for memory, the table containsk/4 elements, wherekis the number of input samples in one full period of the sine wave.

Dependencies

This parameter is only visible when you set theComputation methodparameter toTable 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 isMT_s, where you specifyMin theSamples per frameparameter.

Dependencies

要启用该参数,设置Sample modetoDiscrete.

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 anM-by-Nmatrix with frame periodMT_s, where you specifyT_sin theSample timeparameter.

Dependencies

要启用该参数,设置Sample modetoDiscrete.

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 theSine Waveblock 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 theSine Waveblock is located inside an enabled subsystem and theStates when enablingparameter of theEnable(Simulink)block is set toreset.

Data Types

Output data type—Output data type
`double`(default) |`single`|`fixdt(1,16)`|`fixdt(1,16,0)`||`Inherit:Inherit via back propagation`

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

Inherit— Lets you specify a rule for inheriting a data type, for example,通过反向传播继承:继承
Built in— Lets you specify a built in data type, for example,double
修复ed 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`|`修复ed point`|`Expression`

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

Inherit— Lets you specify a rule for inheriting a data type, for example,通过反向传播继承:继承
Built in— Lets you specify a built-in data type, for example,double
修复ed 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, seeSpecify 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, seeSpecify Data Types Using Data Type Assistant(Simulink).

Limitations

TheSine Waveonly supportsSigneddata 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, seeSpecify Data Types Using Data Type Assistant(Simulink).

Dependencies

要启用该参数,设置Modeto修复ed 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, seeSpecify Data Types Using Data Type Assistant(Simulink).

Dependencies

要启用该参数,设置Modeto修复ed 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

要启用该参数,设置Modeto修复ed pointandScalingtoBinary 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

要启用该参数,设置ModetoBuilt inor修复ed point. For more information, seeSpecify 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

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When you selectDiscretefrom theSample modeparameter, the secondaryComputation methodparameter provides three options for generating the discrete sinusoid:Trigonometric fcn,Table lookup, andDifferential.

Trigonometric Fcn

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

$\begin{array}{l} y_{i} = A_{i} \sin (2 π f_{i} t + ϕ_{i}) & (real) \\ \begin{array}{l} or \end{array} \\ y_{i} = A_{i} e^{j (2 π f_{i} t + ϕ_{i})} & (complex) \end{array}$

with a period ofT_s, where you specifyT_sin theSample timeparameter. This mode of operation has the same benefits and liabilities as theContinuoussample mode.

At each sample time, the block evaluates the sine function at the appropriate time valuewithin the first cycleof 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 theuniquesamples 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_imust be an integer value for every channeli= 1, 2, ...,N.

When theOptimize table forparameter is set toSpeed, the table constructed for each channel containsk_ielements. When theOptimize table forparameter is set toMemory, the table constructed for each channel containsk_i/4 elements.

长时间了put 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 theTable lookupcomputation mode, the maximum amount of precision you can achieve in your output is 53 bits. Setting the word length of theOutputorUser-defineddata type to values greater than 53 bits does not improve the precision of your output.

Tip

To generate fixed-point sinusoids, you must selectTable 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.

$\begin{array}{l} \sin (t + T_{s}) = \sin (t) \cos (T_{s}) + \cos (t) \sin (T_{s}) \\ \cos (t + T_{s}) = \cos (t) \cos (T_{s}) - \sin (t) \sin (T_{s}) \end{array}$

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

$[\begin{matrix} \sin {2 π f_{i} (t + T_{s}) + ϕ_{i}} \\ \cos {2 π f_{i} (t + T_{s}) + ϕ_{i}} \end{matrix}] = [\begin{matrix} \cos (2 π f_{i} T_{s}) & \sin (2 π f_{i} T_{s}) \\ - \sin (2 π f_{i} T_{s}) & \cos (2 π f_{i} T_{s}) \end{matrix}] [\begin{matrix} \sin (2 π f_{i} t + ϕ_{i}) \\ \cos (2 π f_{i} t + ϕ_{i}) \end{matrix}]$

你指定T_sin theSample timeparameter. SinceT_sis constant, the right-hand matrix is a constant and can be computed once at the start of the simulation. The value ofA_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™.

TheSine Waveblock references absolute simulation time when configured in continuous sample mode.

HDL Code Generation
Generate Verilog and VHDL 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, seeNCO(DSP HDL Toolbox), andGenerate 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 followingSine Waveblock settings:

Computation method:Table lookup
Sample mode:Discrete

Output:

The output port cannot have data typessingleordouble.

Complex Data Support

This block supports code generation for complex signals.

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

If the input is fixed point, it must be a signed integer or a signed fixed point value with a power-of-two slope and zero bias.

Version History

Introduced before R2006a

Sine Wave

Description

Generating Multichannel Outputs

Examples

Generate Frame-Based Sine Waves

Generate Sample-Based Sine Waves

Ports

Output

Port_1—Sinusoidal signalscalar | vector | matrix

Parameters

Main

Amplitude—Amplitude of sine waves1(default) | scalar | vector

Frequency (Hz)—Frequency of each sine wave100(default) | scalar | vector

Phase offset (rad)—Phase offset0(default) | scalar | vector

Sample mode—Continuous or discrete sampling modeDiscrete(default) |Continuous

Output complexity—Real or complex waveformReal(default) |Complex

Computation method—Method for computing discrete-time sinusoidsTrigonometric fcn(default) |Table lookup|Differential

Dependencies

Optimize table for—优化速度或内存Speed(default) |Memory

Dependencies

Sample time—Sample period1/1000(default) | scalar

Dependencies

Samples per frame—Samples per frame1(default) | positive integer

Dependencies

Resetting states when re-enabled—State behavior inside enabled subsystemsRestart at time zero(default) |Catch up to simulation time

Dependencies

Data Types

Output data type—Output data typedouble(default) |single|fixdt(1,16)|fixdt(1,16,0)||Inherit:Inherit via back propagation

Data Type Assistant

Mode—Data type modeBuilt in(default) |Inherit|修复ed point|Expression

Signedness—Signedness of fixed-point dataSigned(default)

Limitations

Scaling—Method for scaling fixed-point dataBest precision(default) |Binary point

Dependencies

Word length—Bit size of the word that holds the quantized integer16(default) | integer from 2 to 128

Dependencies

Fraction length—Fraction length for fixed-point data type0(default) | integer scalar

Dependencies

Data type override—Data type override modeInherit(default) |Off

Dependencies

Block Characteristics

Algorithms

Trigonometric Fcn

Table Lookup

Differential

Extended Capabilities

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

HDL Code GenerationGenerate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

修复ed-Point ConversionDesign and simulate fixed-point systems using Fixed-Point Designer™.

Version History

See Also

Blocks

Functions

Objects

Port_1—Sinusoidal signal
scalar | vector | matrix

Amplitude—Amplitude of sine waves
`1`(default) | scalar | vector

Frequency (Hz)—Frequency of each sine wave
`100`(default) | scalar | vector

Phase offset (rad)—Phase offset
`0`(default) | scalar | vector

Sample mode—Continuous or discrete sampling mode
`Discrete`(default) |`Continuous`

Output complexity—Real or complex waveform
`Real`(default) |`Complex`

Computation method—Method for computing discrete-time sinusoids
`Trigonometric fcn`(default) |`Table lookup`|`Differential`

Optimize table for—优化速度或内存
`Speed`(default) |`Memory`

Sample time—Sample period
`1/1000`(default) | scalar

Samples per frame—Samples per frame
`1`(default) | positive integer

Resetting states when re-enabled—State behavior inside enabled subsystems
`Restart at time zero`(default) |`Catch up to simulation time`

Output data type—Output data type
`double`(default) |`single`|`fixdt(1,16)`|`fixdt(1,16,0)`||`Inherit:Inherit via back propagation`

Mode—Data type mode
`Built in`(default) |`Inherit`|`修复ed point`|`Expression`

Signedness—Signedness of fixed-point data
`Signed`(default)

Scaling—Method for scaling fixed-point data
`Best precision`(default) |`Binary point`

Word length—Bit size of the word that holds the quantized integer
`16`(default) | integer from 2 to 128

Fraction length—Fraction length for fixed-point data type
`0`(default) | integer scalar

Data type override—Data type override mode
`Inherit`(default) |`Off`

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

HDL Code Generation
Generate Verilog and VHDL code for FPGA and ASIC designs using HDL Coder™.

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