pulseWaveformLibrary

Create library of pulse waveforms

Since R2021a

Description

The pulseWaveformLibrary System object™ creates a library of pulse waveforms. The waveforms in the library can be of different types or be of the same type with different parameters. You can use this library to transmit different kinds of pulses during a simulation.

To make a waveform library

1. Create the pulseWaveformLibrary object and set its properties.

2. Call the object with arguments, as if it were a function.

To learn more about how System objects work, see What Are System Objects?

Creation

Syntax

pulselib = pulseWaveformLibrary

pulselib = pulseWaveformLibrary(Name,Value)

Description

pulselib = pulseWaveformLibrary System object creates a library of pulse waveforms, pulselib, with default property values. The default consists of a rectangular waveform and a linear FM waveform.

pulselib = pulseWaveformLibrary(Name,Value) creates a pulse waveform library with each property Name set to a specified Value. You can specify additional name-value pair arguments in any order as (Name1,Value1,...,NameN,ValueN). Enclose each property name in single quotes.

Example: pulselib = pulseWaveformLibrary('SampleRate',1e9,'WaveformSpecification',{{'Rectangular','PRF',1e4,'PulseWidth',100e-6},{'SteppedFM','PRF',1e4}}) creates a library containing one rectangular waveform and one stepped-FM waveform, both sampled at 1 GHz.

Properties

Unless otherwise indicated, properties are nontunable, which means you cannot change their values after calling the object. Objects lock when you call them, and the release function unlocks them.

If a property is tunable, you can change its value at any time.

For more information on changing property values, see System Design in MATLAB Using System Objects.

SampleRate — Waveform sample rate

1e6 (default) | positive scalar

Waveform sample rate, specified as a positive scalar. All waveforms have the same sample rate. Units are in hertz.

Example: 100e3

Data Types: double

WaveformSpecification — Pulse waveforms

{{'Rectangular','PRF',10e3,'PulseWidth',100e-6},{'LinearFM','PRF',1e4,'PulseWidth',50e-6,'SweepBandwidth',1e5,'SweepDirection','Up','SweepInterval','Positive'}} (default) | cell array

Pulse waveforms, specified as a cell array. Each cell of the array contains the specification of one waveform.

{{Waveform 1 Specification},{Waveform 2 Specification},{Waveform 3 Specification}, ...}

Each waveform specification is also a cell array containing the parameters of the waveform. The entries in a specification cell are the pulse identifier and a set of name-value pairs specific to that waveform.

{PulseIdentifier,Name1,Value1,Name2,Value2, ...}

This System object supports four built-in waveforms and also lets you specify custom waveforms. For the built-in waveforms, the waveform specifier consists of a waveform identifier followed by several name-value pairs setting the properties of the waveform. For the custom waveforms, the waveform specifier consists of a handle to a user-define waveform function and the functions input arguments.

Waveform Types

Waveform type	Waveform identifier	Waveform arguments
Linear FM	'LinearFM'	Linear FM Waveform Arguments
Phase coded	'PhaseCoded'	Phase-Coded Waveform Arguments
Rectangular	'Rectangular'	Rectangular Waveform Arguments
Stepped FM	'SteppedFM'	Stepped FM Waveform Arguments
Custom	Function handle	Custom Waveform Arguments

Example: {{'Rectangular','PRF',10e3,'PulseWidth',100e-6},{'Rectangular','PRF',100e3,'PulseWidth',20e-6}}

Data Types: cell

Linear FM Waveform Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: {'LinearFM','PRF',1e4,'PulseWidth',50e-6,'SweepBandwidth',1e5,... 'SweepDirection','Up','SweepInterval','Positive'}

PRF — Pulse repetition frequency

1e4 (default) | positive scalar

Pulse repetition frequency (PRF), specified as a positive scalar. Units are in hertz. See Pulse Repetition Frequency Restrictions for restrictions on the PRF.

Example: 20e3

Data Types: double

PulseWidth — Pulse duration

5e-5 (default) | positive scalar

Pulse duration, specified as a positive scalar. Units are in seconds. You cannot specify both PulseWidth and DutyCycle.

Example: 100e-6

Data Types: double

DutyCycle — Pulse duty cycle

0.5 | positive scalar

Pulse duty cycle, specified as a positive scalar greater than zero and less than or equal to one. You cannot specify both PulseWidth and DutyCycle.

Example: 0.7

Data Types: double

SweepBandwidth — Bandwidth of the FM sweep

1e5 (default) | positive scalar

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

Example: 100e3

Data Types: double

SweepDirection — Bandwidth of the FM sweep

'Up' (default) | 'Down'

Direction of the FM sweep, specified as 'Up' or 'Down'. 'Up' corresponds to increasing frequency. 'Down' corresponds to decreasing frequency.

Data Types: char

SweepInterval — FM sweep interval

'Positive' (default) | 'Symmetric'

FM sweep interval, specified as 'Positive' or 'Symmetric'. If you set this property value to 'Positive', the waveform sweeps the interval between 0 and B, where B is the SweepBandwidth argument value. If you set this property value to 'Symmetric', the waveform sweeps the interval between –B/2 and B/2.

Example: 'Symmetric'

Data Types: char

Envelope — Envelope function

'Rectangular' (default) | 'Gaussian'

Envelope function, specified as 'Rectangular' or 'Gaussian'.

Example: 'Gaussian'

Data Types: char

FrequencyOffset — Frequency offset of pulse

0 (default) | scalar

Frequency offset of pulse, specified as a scalar. The frequency offset shifts the frequency of the generated pulse waveform. Units are in hertz.

Example: 100e3

Data Types: double

Phase-Coded Waveform Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: {'PhaseCoded','PRF',1e4,'Code','Zadoff-Chu', 'SequenceIndex',3,'ChipWidth',5e-6,'NumChips',8}

PRF — Pulse repetition frequency

1e4 (default) | positive scalar

Pulse repetition frequency (PRF), specified as a positive scalar. Units are in hertz. See Pulse Repetition Frequency Restrictions for restrictions on the PRF.

Example: 20e3

Data Types: double

Code — Type of phase modulation code

'Frank' (default) | 'P1' | 'P2''Px' | 'Zadoff-Chu' | 'P3' | 'P4' | 'Barker'

Type of phase modulation code, specified as 'Frank', 'P1', 'P2', 'Px', 'Zadoff-Chu', 'P3', 'P4', or 'Barker'.

Example: 'P1'

Data Types: char

SequenceIndex — Zadoff-Chu sequence index

1 (default) | positive integer

Sequence index used for the Zadoff-Chu code, specified as a positive integer. The value of SequenceIndex must be relatively prime to the value of NumChips.

Example: 3

Dependencies

To enable this name-value pair, set the Code property to 'Zadoff-Chu'.

Data Types: double

ChipWidth — Chip duration

1e-5 (default) | positive scalar

Chip duration, specified as a positive scalar. Units are in seconds. See Chip Restrictions for restrictions on chip sizes.

Example: 30e-3

Data Types: double

NumChips — Number of chips in waveform

4 (default) | positive integer

Number of chips in waveform, specified as a positive integer. See Chip Restrictions for restrictions on chip sizes.

Example: 3

Data Types: double

FrequencyOffset — Frequency offset of pulse

0 (default) | scalar

Frequency offset of pulse, specified as a scalar. The frequency offset shifts the frequency of the generated pulse waveform. Units are in hertz.

Example: 100e3

Data Types: double

Rectangular Waveform Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: {'Rectangular','PRF',10e3,'PulseWidth',100e-6}

PRF — Pulse repetition frequency

1e4 (default) | positive scalar

Pulse repetition frequency (PRF), specified as a positive scalar. Units are in hertz. See Pulse Repetition Frequency Restrictions for restrictions on the PRF.

Example: 20e3

Data Types: double

PulseWidth — Pulse duration

5e-5 (default) | positive scalar

Pulse duration, specified as a positive scalar. Units are in seconds. You cannot specify both PulseWidth and DutyCycle.

Example: 100e-6

Data Types: double

DutyCycle — Pulse duty cycle

0.5 | positive scalar

Pulse duty cycle, specified as a positive scalar greater than zero and less than or equal to one. You cannot specify both PulseWidth and DutyCycle.

Example: 0.7

Data Types: double

FrequencyOffset — Frequency offset of pulse

0 (default) | scalar

Frequency offset of pulse, specified as a scalar. The frequency offset shifts the frequency of the generated pulse waveform. Units are in hertz.

Example: 100e3

Data Types: double

Stepped FM Waveform Arguments

Specify optional pairs of arguments as Name1=Value1,...,NameN=ValueN, where Name is the argument name and Value is the corresponding value. Name-value arguments must appear after other arguments, but the order of the pairs does not matter.

Before R2021a, use commas to separate each name and value, and enclose Name in quotes.

Example: {'SteppedFM','PRF',10e-4}

PRF — Pulse repetition frequency

1e4 (default) | positive scalar

Pulse repetition frequency (PRF), specified as a positive scalar. Units are in hertz. See Pulse Repetition Frequency Restrictions for restrictions on the PRF.

Example: 20e3

Data Types: double

PulseWidth — Pulse duration

5e-5 (default) | positive scalar

Pulse duration, specified as a positive scalar. Units are in seconds. You cannot specify both PulseWidth and DutyCycle.

Example: 100e-6

Data Types: double

DutyCycle — Pulse duty cycle

0.5 | positive scalar

Pulse duty cycle, specified as a positive scalar greater than zero and less than or equal to one. You cannot specify both PulseWidth and DutyCycle.

Example: 0.7

Data Types: double

NumSteps — Number of frequency steps in waveform

5 (default) | positive integer

Number of frequency steps in waveform, specified as a positive integer.

Example: 3

Data Types: double

FrequencyStep — Linear frequency step size

20e3 (default) | positive scalar

Linear frequency step size, specified as a positive scalar.

Example: 100.0

Data Types: double

FrequencyOffset — Frequency offset of pulse

0 (default) | scalar

Frequency offset of pulse, specified as a scalar. The frequency offset shifts the frequency of the generated pulse waveform. Units are in hertz.

Example: 100e3

Data Types: double

Custom Waveform Arguments

You can create a custom waveform from a user-defined function. The first input argument of the function must be the sample rate. For example, specify a hyperbolic waveform function,

function wav = HyperbolicFM(fs,prf,pw,freq,bw,fcent),

where fs is the sample rate and prf, pw, freq, bw, and fcent are other waveform arguments. The function must have at least one output argument, wav, to return the samples of each pulse. This output must be a column vector. There can be other outputs returned following the waveform samples.

Then, create a waveform specification using a function handle instead of the waveform identifier. The first cell in the waveform specification must be a function handle. The remaining cells contain all function input arguments except the sample rate. Specify all input arguments in the order they are passed into the function.

waveformspec = {@HyperbolicFM,prf,pw,freq,bw,fcent}

See Add Custom Waveform to Pulse Waveform Library for an example that uses a custom waveform.

Usage

Syntax

waveform = pulselib(idx)

Description

waveform = pulselib(idx) returns samples of a waveform, waveform, specified by its index, idx, in the library.

Input Arguments

idx — Index of the waveform in the waveform library

positive integer

Index of the waveform in the waveform library, specified as a positive integer.

Example: 2

Data Types: double

Output Arguments

waveform — Waveform samples

complex-valued vector

Waveform samples, returned as a complex-valued vector.

Data Types: double
Complex Number Support: Yes

Object Functions

To use an object function, specify the System object as the first input argument. For example, to release system resources of a System object named obj, use this syntax:

release(obj)

Specific to pulseWaveformLibrary

getMatchedFilter	Matched filter coefficients for pulse waveform
plot	Plot waveform from waveform library

Common to All System Objects

step	Run System object algorithm
release	Release resources and allow changes to System object property values and input characteristics
reset	Reset internal states of System object

Examples

Obtain and Plot Phase-Coded Waveform from Waveform Library

Construct a waveform library consisting of three waveforms. The library contains a rectangular, a linear FM, and a phase-coded waveform. Then, obtain and plot the real and imaginary parts of the phase-coded waveform.

waveform1 = {'Rectangular','PRF',1e4,'PulseWidth', 50e-6};
waveform2 = {'LinearFM','PRF',1e4,'PulseWidth',50e-6, ...
    'SweepBandwidth',1e5,'SweepDirection','Up',...
    'SweepInterval', 'Positive'};
waveform3 = {'PhaseCoded','PRF',1e4,'Code','Zadoff-Chu', ...
    'SequenceIndex',3,'ChipWidth',5e-6,'NumChips',8};
fs = 1e6;
wavlib = pulseWaveformLibrary('SampleRate',fs, ...
    'WaveformSpecification',{waveform1,waveform2,waveform3});

Extract the waveform from the library.

wav3 = wavlib(3);

Plot the waveform using the plot method.

plot(wavlib,3,'PlotType','complex')

Plot Stepped FM Waveform

Construct a waveform library consisting of three waveforms. The library contains one rectangular, one linear FM, and one stepped-FM waveforms. Then, plot the real parts of the first three pulses of the stepped-fm waveform.

waveform1 = {'Rectangular','PRF',1e4,'PulseWidth',70e-6};
waveform2 = {'LinearFM','PRF',1e4,'PulseWidth',70e-6, ...
    'SweepBandwidth',1e5,'SweepDirection','Up', ...
    'SweepInterval', 'Positive'};
waveform3 = {'SteppedFM','PRF',1e4,'PulseWidth', 70e-6,'NumSteps',5, ...
    'FrequencyStep',50000,'FrequencyOffset',0};
fs = 1e6;
wavlib = pulseWaveformLibrary('SampleRate',fs, ...
    'WaveformSpecification',{waveform1,waveform2,waveform3});

Plot the first three pulses of the waveform using the plot method.

plot(wavlib,3,'PulseIdx',1)

plot(wavlib,3,'PulseIdx',2)

plot(wavlib,3,'PulseIdx',3)

Plot Matched Filter Coefficients of Two Pulses

This example shows how to put two waveforms into a waveform library and how to extract and plot their matched filter coefficients.

Create a pulse library consisting of a rectangular and a linear FM waveform.

waveform1 = {'Rectangular','PRF',10e3 'PulseWidth',50e-6};
waveform2 = {'LinearFM','PRF',10e3,'PulseWidth',50e-6,'SweepBandwidth',1e5, ...
    'SweepDirection','Up','SweepInterval', 'Positive'};
pulsesib = pulseWaveformLibrary('SampleRate',1e6,...
    'WaveformSpecification',{waveform1,waveform2});

Retrieve the matched filter coefficients for each waveform and plot their real parts.

coeff1 = getMatchedFilter(pulsesib,1,1);
subplot(2,1,1)
stem(real(coeff1))
title('Matched filter coefficients, real part')
coeff2 = getMatchedFilter(pulsesib,2,1);
subplot(2,1,2)
stem(real(coeff2))
title('Matched filter coefficients, real part')

Add Custom Waveform to Pulse Waveform Library

Define a custom hyperbolic FM waveform and add it to a pulseWaveformLibrary System object together with a linear FM waveform. Plot the hyperbolic waveform.

Specify the hyperbolic FM waveform parameters. The pulse width is 75 ms and the pulse repetition interval is 100 ms. The center frequency is 500 Hz and the bandwidth is 400 Hz.

fs = 50e3;
pri = 0.1;
prf = 1/pri;
pw = 0.075;
bw = 400.0;
fcent = 500.0;

Create a pulse waveform library consisting of a hyperbolic FM waveform and a linear FM waveform.

pulselib = pulseWaveformLibrary('SampleRate',fs, ...
    'WaveformSpecification',{{@HyperbolicFM,prf,pw,bw,fcent}, ...
    {'LinearFM','PRF',prf,'PulseWidth',pw, ...
    'SweepBandwidth',bw,'SweepDirection','Up',...
    'SweepInterval','Positive'}});

Plot the complex hyperbolic FM waveform.

plot(pulselib,1,'PlotType','complex')

Define the Hyperbolic FM waveform function.

function y = HyperbolicFM(fs,prf,pw,bw,fcent)
pri = 1/prf;
t = [0:1/fs:pri]';
idx = find(t <= pw);
fl = fcent - bw/2;
fh = fcent + bw/2;
y = zeros(size(t));
arg = 2*pi*fl*fh/bw*pw*log(1.0 - bw*t(idx)/fh/pw);
y(idx) = exp(1i*arg);
end

More About

Pulse Repetition Frequency Restrictions

The PRF property must satisfy these restrictions:

• The product of PRF and PulseWidth must be less than or equal to one. This condition expresses the requirement that the pulse width is less than one pulse repetition interval.

• The ratio of SampleRate to PRF must be an integer. This condition expresses the requirement that the number of samples in one pulse repetition interval is an integer.

Chip Restrictions

The values of the ChipWidth and NumChips properties must satisfy these constraints:

• The product of PRF, ChipWidth, and NumChips must be less than or equal to one. This condition expresses the requirement that the sum of the durations of all chips is less than one pulse repetition interval.

• The product of SampleRate and ChipWidth must be an integer. This condition expresses the requirement that the number of samples in a chip must be an integer.

The table shows additional constraints on the number of chips for different code types.

If the Code Property Is ...	Then the NumChips Property Must Be...
'Frank', 'P1', or 'Px'	A perfect square
'P2'	An even number that is a perfect square
'Barker'	2, 3, 4, 5, 7, 11, or 13

Extended Capabilities

C/C++ Code Generation

Generate C and C++ code using MATLAB® Coder™.

Usage notes and limitations:

The plot object function is not supported.

See System Objects in MATLAB Code Generation (MATLAB Coder).

Version History

Introduced in R2021a