EXERCISE 11.1.
A chirp signal, whose instantaneous frequency linearly sweeps the band between f1 and f2, is expressed as follows:
s(t) = sin[(2πf1 + 2πβt)t+Φ0]
with β = (f2 – f1)/(2PulseLength), Pulselength being the signal duration.
a.
% Generation of a linear frequency modulated signal f1=2000; f2=8000; pulselength=0.025; Fs=20000; % Sampling frequency % Warning: Fs should verify the Nyquist constraint: Fs>2*max(f1,f2) t=(0:1/Fs:pulselength); beta=(f2-f1)/ (2*pulselength); chirp1=sin(2*pi*(f1+beta*t).*t); % Another way to generate the chirp signal chirp2 = vco(sawtooth((2*pi/pulselength)*t,1), [f1/Fs,f2/Fs]*Fs,Fs); % chirpl and chirp2 are similar up to a phase term
b.
figure; clf; subplot (211) plot(t,chirp1); xlabel( 'Time [s]'); ylabel('Amplitude'); title(' Time variation of a chirp signal') C=fftshift (abs(fft(chirp1) ).^2); lc=length(chirpl); mc=lc/2; freq=(-mc:1:mc-1)*Fs/lc; subplot (212) plot (freq,C); xlabel('Frequency [Hz]'); ylabel('Power ...
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