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Instantaneous frequency of nonlinear frequency-modulated waveform

Since R2023a



    freq = nlfmspec2freq(BW,S) returns samples of the instantaneous frequency freq for a nonlinear frequency modulated (NLFM) pulse waveform. The waveform sweeps the bandwidth BW and has a power spectrum shape S. The frequency values in freq are found by applying the principle of stationary phase to the power spectrum shape S.


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    Create a nonlinear FM waveform derived from a power spectral density function shaped as a Taylor window with -35 dB sidelobes. The pulse bandwidth is 120 MHz and the pulse duration is10μsec. Generate matched filter coefficients and then apply a matched filter. Plot the resulting matched filter output to display the range sidelobe levels.

    BW = 120e6;
    T = 10e-6;
    fs = 10*BW;

    Generate 200 points of a waveform with instantaneous frequency values defined by a Taylor window. The window has -35 dB sidelobe levels.

    w = taylorwin(200,4,-35);
    freq = nlfmspec2freq(BW,w);
    waveform = phased.CustomFMWaveform('SampleRate',fs, ...
        'PulseWidth',T,'FrequencyModulation',freq, ...
    disp(['Bandwidth = ',num2str(bandwidth(waveform)/1e6),' MHz']);
    Bandwidth = 119.9644 MHz

    Obtain the matched filter coefficients from the waveform.

    [wav,coeff] = waveform();
    filter = phased.MatchedFilter('CoefficientsSource','Input port');
    mfout = filter(wav,coeff);

    Plot input signal and matched filter output.

    t = (0:numel(wav)-1)/fs;
    xlabel('Time (\mus)')
    ylabel('Amplitude (V)')
    title('Input Signal')
    xlabel('Time (\mus)')
    ylabel('Amplitude (dB)')
    title('Matched Filter Output')
    xlim([9 11]);
    ylim([0 100]);

    Input Arguments

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    Pulse waveform bandwidth, specified as a positive scalar. Units are in Hz.

    Example: 10e3

    Data Types: double

    Power spectrum shape, specified as a real-valued vector. Units are dimensionless.

    Data Types: double

    Output Arguments

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    Instantaneous waveform frequencies, returned as a real-valued row vector. The instantaneous frequencies form a single up-sweep. freq has the same number of elements as S. Units are Hz.

    Data Types: double


    [1] Collins, T., and P. Atkins. "Nonlinear frequency modulation chirps for active sonar" IEE Proceedings-Radar, Sonar and Navigation 146.6 (1999): 312-316.

    [2] Levanon, Nadav, and Eli Mozeson. Radar signals. John Wiley & Sons, 2004, pp. 92-93.

    [3] Doerry, Armin Walter. "Generating nonlinear FM chirp waveforms for radar". No. SAND2006-5856. Sandia National Laboratories (SNL), Albuquerque, NM, and Livermore, CA (United States), 2006.

    [4] Cook, C. E. "A class of nonlinear FM pulse compression signals." Proceedings of the IEEE 52.11 (1964): 1369-1371.

    Version History

    Introduced in R2023a