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phased.MFSKWaveform System object

MFSK waveform


The multiple frequency shift keying (MFSK) waveform is used in automotive radar to improve simultaneous range and Doppler estimation of multiple targets. The MFSKWaveform System object™ creates the baseband representation of an MFSK waveform. An MFSK waveform consists of two interleaved sequences of increasing frequencies, as described in Algorithms.

To obtain waveform samples:

  1. Define and set up the MFSK waveform. See Construction.

  2. Call step to generate the MFSK waveform samples according to the properties of phased.MFSKWaveform. The behavior of step is specific to each object in the toolbox. The output of the step method is controlled by the OutputFormat property, which has no effect on the properties of the waveform.


Starting in R2016b, instead of using the step method to perform the operation defined by the System object, you can call the object with arguments, as if it were a function. For example, y = step(obj,x) and y = obj(x) perform equivalent operations. When the only argument to the step method is the System object itself, replace y = step(obj) by y = obj().


sMFSK = phased.MFSKWaveform creates an MFSK waveform System object, sMFSK.

sMFSK = phased.MFSKWaveform(Name,Value) creates an MFSK waveform object, sMFSK, with additional properties specified by one or more Name-Value pair arguments. Name must appear inside single quotes (''). You can specify several name-value pair arguments in any order as Name1,Value1,…,NameN,ValueN.


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Sample rate of the signal, specified as a positive scalar. Units are hertz.

Example: 96e6

Data Types: double

MFSK sweep bandwidth, specified as a positive scalar. Units are in hertz. The sweep bandwidth is the difference between the highest and lowest frequencies of either sequence.

Example: 9e7

Data Types: double

Time duration of each frequency step, specified as a positive scalar in seconds.

Example: 0.2e-3

Data Types: double

Total number of frequency steps in a sweep, specified as an even positive integer.

Example: 16

Data Types: double

Chirp offset frequency, specified as a real scalar. Units are in hertz. The offset determines the frequency translation between the two sequences.

Example: 500

Data Types: double

Output signal grouping, specified as one of 'Steps', 'Sweeps', or 'Samples'. This property has no effect on the waveform but determines the output form of the step method.

  • 'Steps' — The output consists of all samples contained in an integer number of frequency steps, NumSteps.

  • 'Samples' — The output consists of an integer number of samples, NumSamples.

  • 'Sweeps' — The output consists of all samples contained in an integer number of sweeps, NumSweeps.

Example: 'Samples'

Data Types: char

Number of samples in output, specified as a positive integer. This property applies only when you set OutputFormat to 'Samples'.

Example: 200

Data Types: double

Number of frequency steps in output, specified as a positive integer. This property applies only when you set OutputFormat to 'Steps'.

Example: 10

Data Types: double

Number of sweeps in output, specified as a positive integer. This property applies only when you set OutputFormat to 'Sweeps'.

Example: 5

Data Types: double


plotPlot continuous MFSK waveform
resetReset states of the MFSK waveform object
stepSamples of continuous MFSK waveform
Common to All System Objects

Create System object with same property values


Expected number of inputs to a System object


Expected number of outputs of a System object


Check locked states of a System object (logical)


Allow System object property value changes


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Construct an MFSK waveform with a sample rate of 1 MHz and a sweep bandwidth of 0.1 MHz. Assume 52 steps with a step time of 4 milliseconds. Set the frequency offset to 1 kHz. There are 4000 samples per step.

fs = 1e6;
fsweep = 1e5;
tstep = 4e-3;
numsteps = 52;
foffset = 1000;
noutputsteps = 4;
sMFSK = phased.MFSKWaveform('SampleRate',fs,...

Plot the real and imaginary components of the second step of the waveform using the plot method. Set the plot color to red.



An MFSK waveform consists of two interleaved stepped-frequency sequences, as shown in this time-frequency diagram.

Each sequence is a set of continuous waveform (CW) signals increasing in frequency. The offset, Foffset, between the two sequences is constant and can be positive or negative. A complete waveform consists of an even number of steps, N, of equal duration, Tstep. Then, each sequence consists of N/2 steps. The sweep frequency, Fsweep, is the difference between the lowest and highest frequency of either sequence. Fsweep is always positive, indicating increasing frequency. The frequency difference between successive steps of each sequence is given by

Fstep = Fsweep/(N/2–1).

The lowest frequency of the first sequence is always 0 hertz and corresponds to the carrier frequency of the bandpass signal. The lowest frequency of the second sequence can be positive or negative and is equal to Foffset. Negative frequencies correspond to bandpass frequencies that are lower than the carrier frequency. The duration of the waveform is given by Tsweep = N *Tstep. The System object properties corresponding to the signal parameters are

Signal ParameterProperty


[1] Meinecke, Marc-Michale, and Hermann Rohling, “Combination of LFMCW and FSK Modulation Principles for Automotive Radar Systems.” German Radar Symposium GRS2000. 2000.

[2] Rohling, Hermann, and Marc-Michale Meinecke. “Waveform Design Principles for Automotive Radar Systems”. CIE International Conference on Radar. 2001.

Extended Capabilities

Introduced in R2015a

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