How do you interpret FFT of an FFT of a discrete signal?
Essentially, what you do is performing the DFT twice. Performing DFT twice amounts to time-reversing the signal:

N = 16; sN= np.sqrt(N)
x = np.random.randn(N)

X = np.fft.fft(x) / sN

x2 = np.fft.fft(X) / sN

plt.plot(x.real)
plt.plot(x2.real)




blue is original signal, green is two-times DFT. As you can see, the signals are time-reversed in the sense of $y[n]=x[-n \mod N]=x[N-n], n=0...N-1$. (y is green, x is blue). Here, I used the unitary version of the DFT, to keep the signals in the same scale. Otherwise, with the "normal" definition of DFT, the green signal would be scaled by 16.