# Chirp pulse train FFT

I'm trying to understand why the Fourier transform of a chirp pulse train looks the way it does. I will attach the result I get in MATLAB at the end of the question. I tried to develop analytically and I didn't understand if it made sense. In addition, I would also like an explanation for the Fourier transform of a single pulse. I would appreciate your help, thanks!

for one chirp pulse fft the result is (bandwidth = 100MHz):

– Jdip
Commented Jan 13 at 12:43
• Here's a post that talks about how the LFM spectrum comes to be and goes into how the length of the signal determines how the ripples over the passband look: dsp.stackexchange.com/a/70080/26009 Commented Jan 13 at 16:44
• Related if of interest on using a Tukey window to generate a flat response over nearly the full Nyquist range as the FFT of a chirp complete with Python code: dsp.stackexchange.com/a/66545/21048 Commented Jan 13 at 21:33

$$y_p[n] = \sum_k x[n]*\delta[n-kM] \tag{1}$$
where $$*$$ is the convolution operator and $$M$$ the period. Now the Fourier Transform of a pulse train is also a pulse train and convolution on the time domain is multiplication in the frequency domain.