Convert magnitude and/or a phase angle signal to complex signal (2024)

Convert magnitude and/or a phase angle signal to complex signal

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Libraries:
Simulink / Math Operations
HDL Coder / HDL Floating Point Operations

Description

Supported Operations

The Magnitude-Angle to Complex block converts magnitude and phase angleinputs to a complex output. The angle input must be in rad.

When there are two block inputs, the block supports these combinations of inputdimensions:

Two inputs of equal dimensions
One scalar input and the other an n-dimensional array

If the block input is an array, the output is an array of complex signals. The elements of a magnitude input vector map to the magnitudes of the corresponding complex output elements. Similarly, the elements of an angle input vector map to the angles of the corresponding complex output elements. If one input is a scalar, it maps to the corresponding component (magnitude or angle) of all the complex output signals.

Effect of Out-of-Range Input on CORDIC Approximations

If you use the CORDIC approximation method [1],the block input for phase angle has these restrictions:

For signed fixed-point types, the input angle must fall within the range[–2π, 2π) rad.
For unsigned fixed-point types, the input angle must fall within the range[0, 2π) rad.

This table summarizes the effects of an out-of-range input:

Block Usage	Effect of Out-of-Range Input
Simulation modes	An error appears.
Generated code	Undefined behavior occurs.

When you use the CORDIC approximation, ensure that you use an in-range input for theMagnitude-Angle to Complex block. Avoid relying on undefinedbehavior for generated code or accelerator modes.

Examples

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Construct Complex Signal from Magnitude and Phase Angle

Open Model

This example shows how to use the Magnitude-Angle to Complex block to construct a complex-valued signal. You can provide both the magnitude and phase angle as block inputs, or provide one value as an input, and the other on the block dialog box.

Ports

Input

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|u| — Magnitude
scalar | vector | matrix

Magnitude, specified as a real-valued scalar, vector, or matrix.

Dependencies

To enable this port, set Input toMagnitude and angle.

Limitations

If one input has a floating-point data type, the otherinput must use the same data type. For example, both signalsmust be double orsingle.
See Also
Magnitude and phase angle of complex signal Bode plot of frequency response, or magnitude and phase data
Fixed-point data types are supported only when you set theApproximation method toCORDIC. When one input has afixed-point data type, the other input must also have afixed-point data type.

∠u — Radian phase angle
scalar | vector | matrix

Radian phase angle, specified as a real-valued scalar, vector, ormatrix. To compute the CORDIC approximation, the input angle must bebetween:

[–2π, 2π) rad, for signed fixed-point types
[0, 2π) rad, for unsigned fixed-point types

For more information, see Effect of Out-of-Range Input on CORDIC Approximations.

Dependencies

To enable this port, set Input toMagnitude and angle.

Limitations

If one input has a floating-point data type, the otherinput must use the same data type. For example, both signalsmust be double orsingle.
Fixed-point data types are supported only when you set theApproximation method toCORDIC. If one input has afixed-point data type, the other input must also have afixed-point data type.

Port_1 — Magnitude or radian phase angle
scalar | vector | matrix

Magnitude, or radian phase angle, specified as a real-valued scalar,vector, or matrix.

When you set Input toMagnitude, you specify themagnitude at the input port, and the angle on the dialogbox.
When you set Input toAngle, you specify the angle atthe input port, and the magnitude on the dialog box.

Dependencies

To enable this port, set Input toMagnitude orAngle.

Output

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Port_1 — Complex signal
scalar | vector | matrix

Complex signal, formed from the magnitude and phase angle youspecify.

If the block input is an array, the output is an array of complexsignals. The elements of a magnitude input vector map to the magnitudesof the corresponding complex output elements. Similarly, the elements ofan angle input vector map to the angles of the corresponding complexoutput elements. If one input is a scalar, it maps to the correspondingcomponent (magnitude or angle) of all the complex output signals.

Data Types: single | double | fixed point

Parameters

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Input — Type of input
`Magnitude` (default) | `Angle` | `Magnitude and angle`

Specify the kind of input: a magnitude input, an angle input, orboth.

Programmatic Use

Block Parameter:Input

Type: character vector

Values:'Magnitude' | 'Angle' | 'Magnitude andangle'

Default:'Magnitude and angle'

Angle — Phase angle of output
`0` (default) | real-valued scalar, vector, or matrix

Constant phase angle of the output signal, in rad. To compute the CORDIC approximation,the input angle must be between:

[–2π, 2π) rad, for signed fixed-point types
[0, 2π) rad, for unsigned fixed-point types

For more information, see Effect of Out-of-Range Input on CORDIC Approximations.

Dependencies

To enable this parameter, set Input toMagnitude.

Programmatic Use

Block Parameter:ConstantPart

Type: character vector

Values: constantscalar

Default:'0'

Magnitude — Magnitude of output
`0` (default) | real-valued scalar, vector, or matrix

Constant magnitude of the output signal, specified as a real-valuedscalar, vector, or matrix.

Dependencies

To enable this parameter, set Input toAngle.

Programmatic Use

Block Parameter:ConstantPart

Type: character vector

Values:real-valued scalar, vector, ormatrix

Default:'0'

Approximation method — CORDIC or none
`None` (default) | `CORDIC`

Specify the type of approximation for computing output.

Approximation Method	Data Types Supported	When to Use This Method
`None` (default)	Floating point	You want to use the default Taylor seriesalgorithm.
`CORDIC`	Floating point and fixed point	You want a fast, approximate calculation.

When you use the CORDIC approximation, follow these guidelines for the inputangle:

For signed fixed-point types, the input angle must fall within therange [–2π, 2π) rad.
For unsigned fixed-point types, the input angle must fall withinthe range [0, 2π) rad.

The block uses the following data type propagation rules:

Data Type of Magnitude Input Approximation Method Data Type of Complex Output

Data Type of Magnitude Input	Approximation Method	Data Type of Complex Output
Floating point	`None` or`CORDIC`	Same as input
Signed, fixed point	`CORDIC`	`fixdt`(1,`WL` + 2,`FL`) where `WL` and`FL` are the word lengthand fraction length of the magnitude
Unsigned, fixed point	`CORDIC`	`fixdt`(1,`WL` + 3,`FL`) where `WL` and`FL` are the word lengthand fraction length of the magnitude

Floating point

None orCORDIC

Same as input

Signed, fixed point

CORDIC

fixdt(1,WL + 2,FL)

where WL andFL are the word lengthand fraction length of the magnitude

Unsigned, fixed point

CORDIC

fixdt(1,WL + 3,FL)

where WL andFL are the word lengthand fraction length of the magnitude

Programmatic Use

Block Parameter:ApproximationMethod

Type: character vector

Values:'None' | 'CORDIC'

Default:'None'

Number of iterations — Number of iterations for CORDIC algorithm
`11` (default) | positive integer, less than or equal to word length of fixed-pointinput

Number of iterations to perform the CORDIC algorithm. The range ofpossible values depends on the data type of the input:

Data Type of Block Inputs	Value You Can Specify
Floating point	A positive integer
Fixed point	A positive integer that does not exceed the word lengthof the magnitude input or the word length of the phase angleinput, whichever value is smaller

Dependencies

To enable this parameter, set Approximationmethod to CORDIC.

Programmatic Use

Block Parameter:NumberOfIterations

Type: character vector

Values: positive integer, lessthan or equal to word length of fixed-point input

Default:'11'

Scale output by reciprocal of gain factor — Scale real and imaginary parts of complex output
`on` (default) | `off`

Select this check box to scale the real and imaginary parts of the complexoutput by a factor of (1/CORDIC gain). This value dependson the number of iterations you specify. As the number of iterations goesup, the value approaches 1.647.

This check box is selected by default, which leads to a more numericallyaccurate result for the complex output, X + iY. However,scaling the output adds two extra multiplication operations, one forX and one for Y.

Dependencies

To enable this parameter, set Approximationmethod to CORDIC.

Programmatic Use

Block Parameter:ScaleReciprocalGainFactor

Type: character vector

Values:'on' | 'off'

Default:'on'

Sample time (-1 for inherited) — Interval between samples
`-1` (default) | scalar | vector

Specify the time interval between samples. To inherit the sample time, set this parameter to -1. For more information, see Specify Sample Time.

Dependencies

This parameter is visible only if you set it to a value other than -1. To learn more, see Blocks for Which Sample Time Is Not Recommended.

Programmatic Use

Block Parameter: SampleTime

Type: string scalar or character vector

Default: "-1"

Block Characteristics

Data Types	`double` \| `single`
Direct Feedthrough	`yes`
Multidimensional Signals	`yes`
Variable-Size Signals	`yes`
Zero-Crossing Detection	`no`

More About

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CORDIC

CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotation-based CORDIC algorithm is one of the most hardware-efficient algorithms available because it requires only iterative shift-add operations (see References). The CORDIC algorithm eliminates the need for explicit multipliers. Using CORDIC, you can calculate various functions such as sine, cosine, arc sine, arc cosine, arc tangent, and vector magnitude. You can also use this algorithm for divide, square root, hyperbolic, and logarithmic functions.

Increasing the number of CORDIC iterations can produce more accurate results, but doing so increases the expense of the computation and adds latency.

References

[1] Volder, Jack E., “The CORDIC Trigonometric Computing Technique.” IRE Transactions on Electronic Computers EC-8 (1959); 330–334.

[2] Andraka, Ray “A Survey of CORDIC Algorithm for FPGA Based Computers.” Proceedings of the 1998 ACM/SIGDA Sixth International Symposium on Field Programmable Gate Arrays. Feb. 22–24 (1998): 191–200.

[3] Walther, J.S., “A Unified Algorithm for Elementary Functions,” Proceedings of the Spring Joint Computer Conference, May 18-20, 1971: 379–386.

[4] Schelin, Charles W., “Calculator Function Approximation,” The American Mathematical Monthly 90, no. 5 (1983): 317–325.

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 HDLimplementation and synthesized logic.

HDL Architecture

This block has multi-cycle implementations that introduce additionallatency in the generated code. To see the added latency, view thegenerated model or validation model. See Generated Model and Validation Model (HDL Coder).

HDL Block Properties

General

HDL Property	Description
ConstrainedOutputPipeline	Number of registers to place at the outputs bymoving existing delays within your design. Distributedpipelining does not redistribute these registers. Thedefault is `0`. For more details, seeConstrainedOutputPipeline (HDL Coder).
InputPipeline	Number of input pipeline stages to insert in thegenerated code. Distributed pipelining and constrainedoutput pipelining can move these registers. The defaultis `0`. For more details, see InputPipeline (HDL Coder).
OutputPipeline	Number of output pipeline stages to insert in thegenerated code. Distributed pipelining and constrainedoutput pipelining can move these registers. The defaultis `0`. For more details, see OutputPipeline (HDL Coder).
LatencyStrategy	Specify whether to map the blocks in your design to`MAX`, `Min`,`CUSTOM`, or`ZERO` latency for fixed-point andfloating-point types. The default is`MAX`. See also LatencyStrategy (HDL Coder).
CustomLatency	When LatencyStrategy is set to`CUSTOM`, use this property tospecify a custom latency value between`ZERO` and `MAX`for fixed-point types. See also LatencyStrategy (HDL Coder).

Native Floating Point

HDL Property	Description
HandleDenormals	Specify whether you want HDL Coder to insert additional logic to handledenormal numbers in your design. Denormal numbers arenumbers that have magnitudes less than the smallestfloating-point number that can be represented withoutleading zeros in the mantissa. The default is`inherit`. See also HandleDenormals (HDL Coder).
InputRangeReduction	Specify whether your input range is bounded orunbounded. If your input range is unbounded, enable thisproperty for HDL Coder to insert additional logic to reduce therange of inputs to `[-pi, pi]`. Thedefault is `on`. See also InputRangeReduction (HDL Coder).
MantissaMultiplyStrategy	Specify how to implement the mantissamultiplication operation during code generation. Byusing different settings, you can control the DSP usageon the target FPGA device. The default is`inherit`. See also MantissaMultiplyStrategy (HDL Coder).

Fixed-Point Support

You can generate code for Magnitude Angle to complex block with fixed-pointdata types as input. To generate the code with fixed-point data types for theblock, set Input to Magnitude andangle and the Approximation method toCORDIC. When using the CORDIC approximationmethod, the block adds additional cycles of latency as given in tablebelow.

Architecture Parameter Additional cycles of latency

Architecture	Parameter	Additional cycles of latency
`Pol2CartCordic`	Number ofiterations Scaleoutput by reciprocal of gainfactor	When Scale output by reciprocal of gainfactor parameter is`off`, Max Latency =Number of iterations +1. When Scale output by reciprocalof gain factor parameter is`on`, Max Latency =Number of iterations +6.

Pol2CartCordic

Number ofiterations

Scaleoutput by reciprocal of gainfactor

When Scale output by reciprocal of gainfactor parameter isoff,

Max Latency =Number of iterations +1.

When Scale output by reciprocalof gain factor parameter ison,

Max Latency =Number of iterations +6.

Restrictions

Fixed-point data types are not supported when you setInput to Magnitude orAngle.

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

The Magnitude-Angle to Complex block supports fixed-point and base integer datatypes when you set Approximation method toCORDIC.

Version History

Introduced before R2006a

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R2024a: Generate HDL code with fixed-point data types

Starting in R2024a, you can generate HDL code for Magnitude-Angle to Complex blockthat uses fixed-point data types as inputs. To generate code with fixed-point datatypes, set the Input block parameter to Magnitudeand angle and the Approximation methodparameter to CORDIC. When using the CORDIC approximationmethod, you can also enable Scale output by reciprocal of gainfactor to scale the real and imaginary parts of the complex output bya gain factor.

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Convert magnitude and/or a phase angle signal to complex signal (2024)

FAQs

How to calculate magnitude and phase angle of a complex number? ›

A complex number z = x+ jy in the second quadrant of the complex plane. −1(x/y). For the fourth quadrant, θ = tan−1(y/x) and θ = −π/2 − tan−1(x/y). Hence, the argument of any z in the strict lower half-plane is −π/2 − tan−1(x/y), and the argument of any z in the strict right half-plane is tan−1(y/x).

What is magnitude and angle to complex? ›

The Magnitude-Angle to Complex block converts magnitude and phase angle inputs to a complex output. The angle input must be in rad. When there are two block inputs, the block supports these combinations of input dimensions: Two inputs of equal dimensions.

Find Out More ›

How to calculate magnitude and phase angle of a complex number using Matlab? ›

[ mag , angle , validOut ] = magAngle( X , validIn ) converts a scalar or vector of complex values X into their component magnitude and phase angles.

Discover More ›

What is magnitude-angle to complex in Simulink? ›

The Magnitude-Angle to Complex block converts magnitude and/or phase angle inputs to a complex-valued output signal. The inputs must be real-valued signals of type double . The angle input is assumed to be in radians. The data type of the complex output signal is double .

Read On ›

How do you convert phase angle? ›

To calculate the phase angle, one typically measures the time difference between corresponding points on the voltage and current waveforms, then converts this time delay into an angle using the formula: phase angle = (time delay / period) * 360 degrees.

Explore More ›

What is the formula for magnitude and angle? ›

MAGNITUDE AND DIRECTION OF A VECTOR

Given a position vector →v=⟨a,b⟩,the magnitude is found by |v|=√a2+b2. The direction is equal to the angle formed with the x-axis, or with the y-axis, depending on the application. For a position vector, the direction is found by tanθ=(ba)⇒θ=tan−1(ba), as illustrated in Figure 8.8.

Discover More Details ›

What is the formula for magnitude of complex? ›

Magnitude of Complex Number For a complex number z = x + jy, we define the magnitude, |z|, as follows: |z| = px2 + y2. The magnitude can be thought of as the distance a complex number z lies from the origin of the complex plane.

Find Out More ›

What is the formula for the phase angle? ›

What is phase angle formula? To find the phase angle at a certain moment in time you must multiply the angular frequency by the time and add the sum of the initial phase: wt+initial phase.

Show Me More ›

What is the magnitude and phase angle plot? ›

The magnitude plot is having magnitude of 0 dB upto ω=1τ rad/sec. From ω=1τ rad/sec, it is having a slope of 20 dB/dec. In this case, the phase plot is having phase angle of 0 degrees up to ω=1τ rad/sec and from here, it is having phase angle of 90⁰. This Bode plot is called the asymptotic Bode plot.

Show Me More ›

What is the magnitude and direction of a complex number? ›

Using Polar coordinate, a complex number is represented as a vector with magnitude and direction. The direction is measured as an angle in radians. Positive angle is measured counterclockwise from the positive real axis. The directed angle is called argument of the complex number.

View Details ›

How do you convert to complex in MATLAB? ›

z = complex( a , b ) creates a complex output, z , from two real inputs, such that z = a + bi . z = complex( x ) returns the complex equivalent of x , such that isreal(z) returns logical 0 ( false ). If x is real, then z is x + 0i .

Keep Reading ›

What is the magnitude angle form of a complex number? ›

Complex Numbers using Polar Form

Thus, a polar form vector is presented as: Z = A ∠±θ, where: Z is the complex number in polar form, A is the magnitude or modulo of the vector and θ is its angle or argument of A which can be either positive or negative.

What is the magnitude of a complex expression in MATLAB? ›

The complex magnitude (or modulus) is the length of a vector from the origin to a complex value plotted in the complex plane. For a complex value, | a + b i | is defined as a 2 + b 2 .

Learn More ›

How do you find the magnitude of a complex number? ›

Discover More Details ›

Convert magnitude and/or a phase angle signal to complex signal (2024)

Description

Supported Operations

Effect of Out-of-Range Input on CORDIC Approximations

Examples

Construct Complex Signal from Magnitude and Phase Angle

Ports

Input

|u| — Magnitudescalar | vector | matrix

Dependencies

Limitations

∠u — Radian phase angle scalar | vector | matrix

Dependencies

Limitations

Port_1 — Magnitude or radian phase angle scalar | vector | matrix

Dependencies

Output

Port_1 — Complex signalscalar | vector | matrix

Parameters

Input — Type of input Magnitude (default) | Angle | Magnitude and angle

Programmatic Use

Angle — Phase angle of output 0 (default) | real-valued scalar, vector, or matrix

Dependencies

Programmatic Use

Magnitude — Magnitude of output 0 (default) | real-valued scalar, vector, or matrix

Dependencies

Programmatic Use

Approximation method — CORDIC or none None (default) | CORDIC

Programmatic Use

Number of iterations — Number of iterations for CORDIC algorithm 11 (default) | positive integer, less than or equal to word length of fixed-pointinput

Dependencies

Programmatic Use

Scale output by reciprocal of gain factor — Scale real and imaginary parts of complex output on (default) | off

Dependencies

Programmatic Use

Sample time (-1 for inherited) — Interval between samples -1 (default) | scalar | vector

Dependencies

Programmatic Use

Block Characteristics

More About

CORDIC

References

Extended Capabilities

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

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

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

Version History

R2024a: Generate HDL code with fixed-point data types

See Also

Topics

MATLAB-Befehl

Americas

Europe

Asia Pacific

FAQs

How to calculate magnitude and phase angle of a complex number? ›

How do you convert to complex in MATLAB? ›

|u| — Magnitude
scalar | vector | matrix

∠u — Radian phase angle
scalar | vector | matrix

Port_1 — Magnitude or radian phase angle
scalar | vector | matrix

Port_1 — Complex signal
scalar | vector | matrix

Input — Type of input
`Magnitude` (default) | `Angle` | `Magnitude and angle`

Angle — Phase angle of output
`0` (default) | real-valued scalar, vector, or matrix

Magnitude — Magnitude of output
`0` (default) | real-valued scalar, vector, or matrix

Approximation method — CORDIC or none
`None` (default) | `CORDIC`

Number of iterations — Number of iterations for CORDIC algorithm
`11` (default) | positive integer, less than or equal to word length of fixed-pointinput

Scale output by reciprocal of gain factor — Scale real and imaginary parts of complex output
`on` (default) | `off`

Sample time (-1 for inherited) — Interval between samples
`-1` (default) | scalar | vector

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™.

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