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 MagnitudeAngle 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 ndimensional 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 OutofRange Input on CORDIC Approximations
If you use the CORDIC approximation method [1],the block input for phase angle has these restrictions:
For signed fixedpoint types, the input angle must fall within the range[–2π, 2π) rad.
For unsigned fixedpoint types, the input angle must fall within the range[0, 2π) rad.
This table summarizes the effects of an outofrange input:
Block Usage  Effect of OutofRange Input 

Simulation modes  An error appears. 
Generated code  Undefined behavior occurs. 
When you use the CORDIC approximation, ensure that you use an inrange input for theMagnitudeAngle 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 MagnitudeAngle to Complex block to construct a complexvalued 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 realvalued scalar, vector, or matrix.
Dependencies
To enable this port, set Input to
Magnitude and angle
.
Limitations
If one input has a floatingpoint data type, the otherinput must use the same data type. For example, both signalsmust be
double
orsingle
.Fixedpoint data types are supported only when you set theApproximation method to
CORDIC
. When one input has afixedpoint data type, the other input must also have afixedpoint data type.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
∠u — Radian phase angle
scalar  vector  matrix
Radian phase angle, specified as a realvalued scalar, vector, ormatrix. To compute the CORDIC approximation, the input angle must bebetween:
[–2π, 2π) rad, for signed fixedpoint types
[0, 2π) rad, for unsigned fixedpoint types
For more information, see Effect of OutofRange Input on CORDIC Approximations.
Dependencies
To enable this port, set Input to
Magnitude and angle
.
Limitations
If one input has a floatingpoint data type, the otherinput must use the same data type. For example, both signalsmust be
double
orsingle
.Fixedpoint data types are supported only when you set theApproximation method to
CORDIC
. If one input has afixedpoint data type, the other input must also have afixedpoint data type.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
Port_1 — Magnitude or radian phase angle
scalar  vector  matrix
Magnitude, or radian phase angle, specified as a realvalued scalar,vector, or matrix.
When you set Input to
Magnitude
, you specify themagnitude at the input port, and the angle on the dialogbox.When you set Input to
Angle
, you specify the angle atthe input port, and the magnitude on the dialog box.
Dependencies
To enable this port, set Input toMagnitude
orAngle
.
Data Types: single
 double
 int8
 int16
 int32
 int64
 uint8
 uint16
 uint32
 uint64
 fixed point
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)  realvalued 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 fixedpoint types
[0, 2π) rad, for unsigned fixedpoint types
For more information, see Effect of OutofRange 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)  realvalued scalar, vector, or matrix
Constant magnitude of the output signal, specified as a realvaluedscalar, vector, or matrix.
Dependencies
To enable this parameter, set Input toAngle
.
Programmatic Use
Block Parameter:ConstantPart 
Type: character vector 
Values:realvalued 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 fixedpoint types, the input angle must fall within therange [–2π, 2π) rad.
For unsigned fixedpoint 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 

Floating point 
 Same as input 
Signed, fixed point 

where 
Unsigned, fixed point 

where 
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 fixedpointinput
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 fixedpoint 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 

Direct Feedthrough 

Multidimensional Signals 

VariableSize Signals 

ZeroCrossing Detection 

More About
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CORDIC
CORDIC is an acronym for COordinate Rotation DIgital Computer. The Givens rotationbased CORDIC algorithm is one of the most hardwareefficient algorithms available because it requires only iterative shiftadd 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 EC8 (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 1820, 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 multicycle 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 
InputPipeline  Number of input pipeline stages to insert in thegenerated code. Distributed pipelining and constrainedoutput pipelining can move these registers. The defaultis 
OutputPipeline  Number of output pipeline stages to insert in thegenerated code. Distributed pipelining and constrainedoutput pipelining can move these registers. The defaultis 
LatencyStrategy  Specify whether to map the blocks in your design to 
CustomLatency  When LatencyStrategy is set to 
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 smallestfloatingpoint number that can be represented withoutleading zeros in the mantissa. The default is 
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 
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 
FixedPoint Support
You can generate code for Magnitude Angle to complex block with fixedpointdata types as input. To generate the code with fixedpoint 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 

Pol2CartCordic  Number ofiterations Scaleoutput by reciprocal of gainfactor  When Scale output by reciprocal of gainfactor parameter is Max Latency =Number of iterations +1. When Scale output by reciprocalof gain factor parameter is Max Latency =Number of iterations +6. 
Restrictions
Fixedpoint data types are not supported when you setInput to Magnitude
orAngle
.
FixedPoint Conversion
Design and simulate fixedpoint systems using FixedPoint Designer™.
The MagnitudeAngle to Complex block supports fixedpoint and base integer datatypes when you set Approximation method toCORDIC
.
Version History
Introduced before R2006a
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R2024a: Generate HDL code with fixedpoint data types
Starting in R2024a, you can generate HDL code for MagnitudeAngle to Complex blockthat uses fixedpoint data types as inputs. To generate code with fixedpoint 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.
See Also
Complex to MagnitudeAngle  Complex to RealImag  RealImag to Complex
Topics
 Complex Signals
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