I think 'spec_ori' & 'spec_shifted' spectrum amplitude and phase are same in below code. Because of 'spectrum shiting property' (What effect does a delay in the time domain have in the frequency domain?). But both are different. why?
K = 4 * 10^10;
Fs = 10 * 10^6;
t_len = 40 * 10^(-6);
t=-t_len/2:1/Fs:t_len/2; % time axis in range
omega = -Fs/2:1/t_len:Fs/2;
chirp = exp(1i*pi*K*t.^2);
spec_ori = fft(chirp);
spec_shifted = fft((chirp .* exp(1i*2*pi*Fs*t)));
plot(angle(spec_ori)-angle(spec_shifted))
fft
implements) is bijective. Hence, if the input is different, the output must be different. So, I really don't see how the shift properties of the DFT let you assert these should be identical; on the contrary, the shift property even defines how these should be different. $\endgroup$ – Marcus Müller Jul 18 '18 at 6:45exp(1i*2*pi*Fs*t)
might not be what you think it is – plot its real and imaginary part) $\endgroup$ – Marcus Müller Jul 18 '18 at 7:02