Magnitude-Angle to Complex

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

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

Description

Supported Operations

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
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 the Magnitude-Angle to Complex block. Avoid relying on undefined behavior 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 to Magnitude and angle.

Limitations

If one input has a floating-point data type, the other input must use the same data type. For example, both signals must be double or single.
Fixed-point data types are supported only when you set the Approximation method to CORDIC. When one input has a fixed-point data type, the other input must also have a fixed-point data type.

∠u — Radian phase angle
scalar | vector | matrix

Radian phase angle, specified as a real-valued scalar, vector, or matrix. 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 port, set Input to Magnitude and angle.

Limitations

If one input has a floating-point data type, the other input must use the same data type. For example, both signals must be double or single.
Fixed-point data types are supported only when you set the Approximation method to CORDIC. If one input has a fixed-point data type, the other input must also have a fixed-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 to Magnitude, you specify the magnitude at the input port, and the angle on the dialog box.
When you set Input to Angle, you specify the angle at the input port, and the magnitude on the dialog box.

Dependencies

To enable this port, set Input to Magnitude or Angle.

Output

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Port_1 — Complex signal
scalar | vector | matrix

Complex signal, formed from the magnitude and phase angle you specify.

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, or both.

Programmatic Use

Block Parameter: Input

Type: character vector

Values:

'Magnitude' | 'Angle' | 'Magnitude and
								angle'

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 to Magnitude.

Programmatic Use

Block Parameter: ConstantPart

Type: character vector

Values: constant scalar

Default: '0'

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

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

Dependencies

To enable this parameter, set Input to Angle.

Programmatic Use

Block Parameter: ConstantPart

Type: character vector

Values:real-valued scalar, vector, or matrix

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 series algorithm.
`CORDIC`	Floating point and fixed point	You want a fast, approximate calculation.

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

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.

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 length and fraction length of the magnitude
Unsigned, fixed point	`CORDIC`	`fixdt`(1, `WL` + 3, `FL`) where `WL` and `FL` are the word length and fraction length of the magnitude

Floating point

None or CORDIC

Same as input

Signed, fixed point

CORDIC

fixdt(1, WL + 2, FL)

where WL and FL are the word length and fraction length of the magnitude

Unsigned, fixed point

CORDIC

fixdt(1, WL + 3, FL)

where WL and FL are the word length and 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-point input

Number of iterations to perform the CORDIC algorithm. The range of possible 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 length of the magnitude input or the word length of the phase angle input, whichever value is smaller

Dependencies

To enable this parameter, set Approximation method to CORDIC.

Programmatic Use

Block Parameter: NumberOfIterations

Type: character vector

Values: positive integer, less than 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 complex output by a factor of (1/CORDIC gain). This value depends on the number of iterations you specify. As the number of iterations goes up, the value approaches 1.647.

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

Dependencies

To enable this parameter, set Approximation method 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

To set the block parameter value programmatically, use the set_param function.

Parameter:	`SampleTime`
Values:	`"-1"` (default) \| scalar or vector in quotes

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 HDL implementation and synthesized logic.

HDL Architecture

This block has multi-cycle implementations that introduce additional latency in the generated code. To see the added latency, view the generated 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 by moving existing delays within your design. Distributed pipelining does not redistribute these registers. The default 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 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 is `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 and floating-point types. The default is `MAX`. See also LatencyStrategy (HDL Coder).
CustomLatency	When LatencyStrategy is set to `CUSTOM`, use this property to specify 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 handle denormal numbers in your design. Denormal numbers are numbers that have magnitudes less than the smallest floating-point number that can be represented without leading zeros in the mantissa. The default is `inherit`. See also HandleDenormals (HDL Coder).
InputRangeReduction	Specify whether your input range is bounded or unbounded. If your input range is unbounded, enable this property for HDL Coder to insert additional logic to reduce the range of inputs to `[-pi, pi]`. The default is `on`. See also InputRangeReduction (HDL Coder).
MantissaMultiplyStrategy	Specify how to implement the mantissa multiplication operation during code generation. By using different settings, you can control the DSP usage on 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-point data types as input. To generate the code with fixed-point data types for the block, set Input to Magnitude and angle and the Approximation method to CORDIC. When using the CORDIC approximation method, the block adds additional cycles of latency as given in table below.

Architecture Parameter Additional cycles of latency

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

Pol2CartCordic

Number of iterations

Scale output by reciprocal of gain factor

When Scale output by reciprocal of gain factor parameter is off,

Max Latency = Number of iterations + 1.

When Scale output by reciprocal of gain factor parameter is on,

Max Latency = Number of iterations + 6.

Restrictions

Fixed-point data types are not supported when you set Input to Magnitude or Angle.

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 data types when you set Approximation method to CORDIC.

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 block that uses fixed-point data types as inputs. To generate code with fixed-point data types, set the Input block parameter to Magnitude and angle and the Approximation method parameter to CORDIC. When using the CORDIC approximation method, you can also enable Scale output by reciprocal of gain factor to scale the real and imaginary parts of the complex output by a gain factor.

Magnitude-Angle to Complex

Description

Supported Operations

Effect of Out-of-Range Input on CORDIC Approximations

Examples

Construct Complex Signal from Magnitude and Phase Angle

Ports

Input

|u| — Magnitude scalar | 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 signal scalar | 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-point input

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 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™.

Version History

R2024a: Generate HDL code with fixed-point data types

See Also

Topics

|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-point input

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™.