Nonlinear FM Waveform

Nonlinear FM pulse waveform

Since R2023a

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  • Nonlinear FM Waveform block

Libraries:
Phased Array System Toolbox / Waveforms

Description

The Nonlinear FM Waveform block generates a nonlinear FM pulse waveform with specified pulse width, pulse repetition frequency (PRF), and sweep bandwidth. The block outputs an integer number of pulses or an integral number of samples.

Ports

Input

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Index to select the pulse repetition frequency (PRF), specified as a positive integer. The index selects the PRF from the predefined vector of values specified by the Pulse repetition frequency (Hz) parameter.

Example: 4

Dependencies

To enable this port, select Enable PRF selection input.

Data Types: double

Frequency offset in Hz, specified as a scalar.

Example: 2e3

Dependencies

To enable this port, set Source of Frequency Offset to Input port.

Data Types: double

Output

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Pulse waveform samples, returned as a complex-valued vector.

Data Types: double

Pulse repetition frequency of current pulse, returned as a positive scalar.

Dependencies

To enable this port, set the Output signal format parameter to Pulses and then select the Enable PRF output parameter.

Data Types: double

Matched filter coefficients, returned as a vector or matrix.

Dependencies

To enable this port, select Enable Matched Filter Coefficients Output.

Data Types: double
Complex Number Support: Yes

Parameters

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To edit block parameters interactively, use the Property Inspector. From the Simulink® Toolstrip, on the Simulation tab, in the Prepare gallery, select Property Inspector.

Sample rate of the output waveform, specified as a positive scalar. The ratio of Sample rate (Hz) to each element in the Pulse repetition frequency (Hz) vector must be an integer. This restriction is equivalent to requiring that the pulse repetition interval is an integral multiple of the sample interval.

Programmatic Use

Block Parameter:SampleRate
Type:double
Values:positive scalar
Default:1e6

Method to set the pulse duration, specified as Pulse width or Duty cycle. When you set this parameter to Pulse width, the pulse duration is set using the Pulse width (s) parameter. When you set this parameter to Duty cycle, the pulse duration is computed from the values of the Pulse repetition frequency (Hz) and Duty Cycle parameters.

Programmatic Use

Block Parameter:DurationSpecification
Type:string
Values:string
Default:'Pulse width'

The duration of each pulse, specified as a positive scalar. Set the product of Pulse width (s) and Pulse repetition frequency to be less than or equal to one. This restriction ensures that the pulse width is smaller than the pulse repetition interval. Units are in seconds.

Example: 300e-6

Dependencies

To enable this parameter, set the Method to specify pulse duration parameter to Pulse width.

Programmatic Use

Block Parameter:PulseWidth
Type:double
Values:string
Default:50e-6

Waveform duty cycle, specified as a scalar in the range [0,1].

Example: 0.7

Dependencies

To enable this parameter, set the Method to specify pulse duration parameter to Duty cycle.

Programmatic Use

Block Parameter:DutyCycle
Type:double
Values:positive scalar
Default:1e6

Pulse repetition frequency, PRF, specified as a scalar or a row vector. Units are in Hz. The pulse repetition interval, PRI, is the inverse of the pulse repetition frequency, PRF. The value of Pulse repetition frequency (Hz) must satisfy these constraints:

  • The product of Pulse width and Pulse repetition frequency (Hz) must be less than or equal to one. This condition expresses the requirement that the pulse width is less than one pulse repetition interval. For the phase-coded waveform, the pulse width is the product of the chip width and number of chips.

  • The ratio of sample rate to any element of Pulse repetition frequency must be an integer. This condition expresses the requirement that the number of samples in one pulse repetition interval is an integer.

You can select the value of PRF by using block parameter settings alone or in conjunction with the input port, PRFIdx.

  • When the Enable PRF selection input parameter is not selected, set the PRF using block parameters.

    • To implement a constant PRF, specify Pulse repetition frequency (Hz) as a positive scalar.

    • To implement a staggered PRF, specify Pulse repetition frequency (Hz) as a row vector with positive values. After the waveform reaches the last element of the vector, the process continues cyclically with the first element of the vector. When PRF is staggered, the time between successive output pulses cycles through the successive values of the PRF vector.

  • When the Enable PRF selection input parameter is selected, you can implement a selectable PRF by specifying Pulse repetition frequency (Hz) as a row vector with positive real-valued entries. But this time, when you execute the block, select a PRF by passing an index into the PRF vector into the PRFIdx port.

In all cases, the number of output samples is fixed when you set the Output signal format to Samples. When you use a varying PRF and set Output signal format to Pulses, the number of output samples can vary.

Programmatic Use

Block Parameter:PRF
Type:double
Values:positive scalar
Default:1e6

Select this parameter to enable the PRFIdx port.

  • When enabled, pass in an index into a vector of predefined PRFs. Set predefined PRFs using the Pulse repetition frequency (Hz) parameter.

  • When not enabled, the block cycles through the vector of PRFs specified by the Pulse repetition frequency (Hz) parameter. If Pulse repetition frequency (Hz) is a scalar, the PRF is constant.

Programmatic Use

Block Parameter:PRFSelectionInputPort
Type:logical
Values:positive scalar
Default:off

Frequency modulation of the nonlinear FM waveform, specified as Polynomial, Hyperbolic, Hybrid Linear-Tangent, or Stepped Price.

  • When set to Polynomial the block generates a waveform with an instantaneous frequency that follows a polynomial function. The coefficients of the polynomial are specified by the Coefficients of a Polynomial FM parameter. The resulting frequency function is normalized such that each pulse sweeps the bandwidth specified in Sweep bandwidth (Hz). The Sweep interval parameter is inactive when Frequency modulation is set to Polynomial.

  • When set to Hyperbolic the block generates a hyperbolic frequency modulated (HFM) waveform. Use the Start frequency of a hyperbolic FM parameter to set the start frequency of the hyperbolic sweep. The Sweep interval parameter is inactive in this case.

  • When set to Hybrid Linear-Tangent the block generates a hybrid NLFM waveform that combines an LFM with a tan-FM as described by Collins and Atkins [1]. The balance between LFM and tan-FM is specified by the Balance between linear FM and tan-FM parameter, and the portion of the tan(x) curve used for tan-FM is specified by the Tangent curve portion parameter.

  • When set to Stepped Price the block generates a stepped version of the Price's NLFM waveform as given by Levanon and Mozeson [2]. The Sweep interval parameter is inactive when Frequency modulation parameter is set to Stepped Price. In this case the sweep bandwidth is determined by the bandwidth factors specified in the Bandwidth factors parameter and the number of frequency steps specified in Number of frequency steps parameter.

Example: Stepped Price

Programmatic Use

Block Parameter:FrequencyModulation
Type:char, string
Values:char. string
Default:Hyperbolic

Data Types: char | string

Coefficients of the polynomial frequency function, specified as a length-(N+1) real-valued vector. The vector represents the coefficients of an N-th degree polynomial. The first entry in the vector is the coefficient of the highest power N of the polynomial. The last entry is the coefficient of the power zero term of the polynomial.

Example: [0.5,1,1,0.5]

Dependencies

To enable this property, set the Frequency modulation parameter to Polynomial.

Programmatic Use

Block Parameter:PolynomialCoefficients
Type:double
Values:vector
Default:[1 0 0]

Data Types: double

Bandwidth of the linear FM sweep, specified as a positive scalar. Units are in Hz.

Example: 50e3

Programmatic Use

Block Parameter:SweepBandwidth
Type:double
Values:positive scalar
Default:100e3

Direction of nonlinear FM sweep as Up (increasing frequency) or Down (decreasing frequency).

Programmatic Use

Block Parameter:SweepDirection
Type:enum
Values:Up, Down
Default:Up

FM frequency sweep interval, specified as Positive or Symmetric. If you set this parameter to Positive, the waveform sweeps the frequency interval between 0 and B, where B is the value of the Sweep bandwidth parameter. If you set this parameter value to Symmetric, the waveform sweeps the interval between –B/2 and B/2.

Programmatic Use

Block Parameter:SweepInterval
Type:enum
Values:Symmetric, Positive
Default:Positive

FM signal amplitude envelope function, specified as Rectangular, Gaussian, Hamming, Chebyshev, Hann, Kaiser, or Taylor.

Programmatic Use

Block Parameter:Envelope
Type:enum
Values:Rectangular, Gaussian, Hamming, Chebyshev, Hann, Kaiser, or Taylor
Default:Rectangular

Source of frequency offset, specified as Property or Input port.

  • When set to Property, the offset is determined by the value of the Frequency Offset parameter.

  • When set to Input port, the offset is determined by the value of the FreqOffset port.

Programmatic Use

Block Parameter:FrequencyOffsetSource
Type:enum
Values:Property, Input Port
Default:Property

Frequency offset, specified as a scalar. Units are in Hz.

Example: 2e3

Dependencies

To enable this parameter set the Source of Frequency Offset parameter to Input port.

Programmatic Use

Block Parameter:FrequencyOffset
Type:double
Values:scalar
Default:0

The format of the output signal, specified as Pulses or Samples.

If you set this parameter to Samples, the output of the block consists of multiple samples. The number of samples is the value of the Number of samples in output parameter.

If you set this parameter to Pulses, the output of the block consists of multiple pulses. The number of pulses is the value of the Number of pulses in output parameter.

Programmatic Use

Block Parameter:OutputFormat
Type:enum
Values:Pulses Samples
Default:Pulses

Number of samples in the block output, specified as a positive integer.

Example: 1000

Dependencies

To enable this parameter, set the Output signal format parameter to Samples.

Programmatic Use

Block Parameter:NumSamples
Type:double
Values:positive scalar
Default:100

Data Types: double

Number of pulses in the block output, specified as a positive integer.

Example: 2

Dependencies

To enable this parameter, set the Output signal format parameter to Pulses.

Programmatic Use

Block Parameter:NumPulses
Type:double
Values:positive scalar
Default:1

Data Types: double

Select this parameter to enable the PRF output port.

Dependencies

To enable this parameter, set Output signal format to Pulses.

Programmatic Use

Block Parameter:PRFOutputPort
Type:enum
Values:off on
Default:off

Select this parameter to enable the Coeff output port.

Programmatic Use

Block Parameter:CoefficientOutputPort
Type:enum
Values:off on
Default:off

Block simulation, specified as Interpreted Execution or Code Generation. If you want your block to use the MATLAB® interpreter, choose Interpreted Execution. If you want your block to run as compiled code, choose Code Generation. Compiled code requires time to compile but usually runs faster.

Interpreted execution is useful when you are developing and tuning a model. The block runs the underlying System object™ in MATLAB. You can change and execute your model quickly. When you are satisfied with your results, you can then run the block using Code Generation. Long simulations run faster with generated code than in interpreted execution. You can run repeated executions without recompiling, but if you change any block parameters, then the block automatically recompiles before execution.

This table shows how the Simulate using parameter affects the overall simulation behavior.

When the Simulink model is in Accelerator mode, the block mode specified using Simulate using overrides the simulation mode.

Acceleration Modes

Block SimulationSimulation Behavior
NormalAcceleratorRapid Accelerator
Interpreted ExecutionThe block executes using the MATLAB interpreter.The block executes using the MATLAB interpreter.Creates a standalone executable from the model.
Code GenerationThe block is compiled.All blocks in the model are compiled.

For more information, see Choosing a Simulation Mode (Simulink).

Programmatic Use

Block Parameter: SimulateUsing
Type: enum
Values: Interpreted Execution, Code Generation
Default: Interpreted Execution

Extended Capabilities

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

Version History

Introduced in R2023a

See Also