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!

Chirp pulse train fft (fc = 10GHz)

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

enter image description here

  • $\begingroup$ Can you post your code please? $\endgroup$
    – Jdip
    Commented Jan 13 at 12:43
  • $\begingroup$ 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 $\endgroup$
    – Envidia
    Commented Jan 13 at 16:44
  • $\begingroup$ 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 $\endgroup$ Commented Jan 13 at 21:33

1 Answer 1


The spectrum of a single chirps is fairly straight forward. It should roughly be 1 between the start end and end frequency of the chirp and 0 everywhere else. On top of that there are some wiggle caused by finite length, windowing, boundary effects, etc. That's exactly what you see.

I assume by "chirp train" you mean a periodic repetition of a single chirp. Periodic repetition can be written as convolution with a pulse train

$$y_p[n] = \sum_k x[n]*\delta[n-kM] \tag{1}$$

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.

Roughly speaking the periodic repetition in time samples the spectrum at integer multiples the repetition rate. Intuitively this makes sense since all periodic functions do have a discrete line spectrum.

The exact shape depends a lot on the specific details (length, spacing, number of repetitions etc.)


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