nlfmspec2freq

Instantaneous frequency of nonlinear frequency-modulated waveform

Since R2023a

Syntax

freq = nlfmspec2freq(BW,S)

Description

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.

Examples

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 is$$10\mu$$sec. 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();
mfilter = phased.MatchedFilter('CoefficientsSource','Input port');
mfout = mfilter(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])

Input Arguments

BW — Pulse waveform bandwidth

positive scalar

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

Example: 10e3

Data Types: double

S — Power spectrum shape

real-valued vector

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

Data Types: double

Output Arguments

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.

Data Types: double

References

[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