frequenvy shifted chirp

shift = 2; 
sChirpShift = exp(1j*pi*gamma*t.^2).*exp(1j*pi*shift*t); 
plot_complex(t, sChirpShift, 'time') 

time shifted chirp

delay = 3; 
SChirpShift = SChirp.*exp(-1j*2*pi*f*delay); 
sChirpShift = ifft(SChirpShift); 
plot_complex(t, sChirpShift) 

up and down sweep chirp

this is zero phase signal

sChirp1 = exp(1j*pi*gamma*t.^2); 
sChirp2 = exp(-1j*pi*gamma*t.^2); 
sChirpM = [sChirp1, sChirp2]; 
N = length(sChirpM); 
plot_complex(0:N-1, sChirpM, 'time') 

SChirpM = fft(sChirpM); 
f = (0:0.5:2*M-0.5)/(T*2*M); 
plot_complex(f, SChirpM, 'freq') 

windowed chirp

sChirp = exp(1j*pi*gamma*t.^2); 
sChirpW = [zeros(1, M), sChirp, zeros(1, M)]; 
t = [(-2*M:-M-1)*T, t, (M:2*M-1)*T]; 
f = (0:4*M-1)/(T*4*M); 
plot_complex(t, sChirpW, 'time') 
SChirpW = fft(sChirpW); 
plot_complex(f, SChirpW, 'freq') 

windowed chirp full simetry

n = -M : M; 
t = n*T; 
sChirp = exp(1j*pi*gamma*t.^2); 
sChirpW = [zeros(1, M-1), sChirp, zeros(1, M)]; 
t = [(-2*M:-M-2)*T, t, (M:2*M-1)*T]; 
f = (0:4*M-1)/(T*4*M); 
plot_complex(t, sChirpW, 'time') 
SChirpW = fft(sChirpW); 
plot_complex(f, SChirpW, 'freq') 

Conclusion

Chirp contain continuous transition between frequencies so it acts like windowed signal with spectral leakage. Can discrete version of the chirp be modified so this leakage is removed?

Published with MATLAB® R2014a