Instantaneous frequency of nonlinear frequency-modulated waveform
returns samples of the instantaneous frequency
freq = nlfmspec2freq(
freq for a nonlinear
frequency modulated (NLFM) pulse waveform. The waveform sweeps the bandwidth
BW and has a power spectrum shape
frequency values in
freq are found by applying the principle of
stationary phase to the power spectrum shape
Waveform Derived from Taylor Spectrum Window
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 issec. 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, ... 'OutputFormat','Pulses','CoefficientsOutputPort',true); 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; figure subplot(121) plot(t*1e6,real(wav)) xlabel('Time (\mus)') ylabel('Amplitude (V)') title('Input Signal') subplot(122) plot(t*1e6,mag2db(abs(mfout))); xlabel('Time (\mus)') ylabel('Amplitude (dB)') title('Matched Filter Output') xlim([9 11]); ylim([0 100]);
BW — Pulse waveform bandwidth
Pulse waveform bandwidth, specified as a positive scalar. Units are in Hz.
S — Power spectrum shape
Power spectrum shape, specified as a real-valued vector. Units are dimensionless.
freq — Instantaneous waveform frequencies
real-valued row vector
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.
 Collins, T., and P. Atkins. "Nonlinear frequency modulation chirps for active sonar" IEE Proceedings-Radar, Sonar and Navigation 146.6 (1999): 312-316.
 Levanon, Nadav, and Eli Mozeson. Radar signals. John Wiley & Sons, 2004, pp. 92-93.
 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.
 Cook, C. E. "A class of nonlinear FM pulse compression signals." Proceedings of the IEEE 52.11 (1964): 1369-1371.
Introduced in R2023a