# Similarity in absolute value of nearby DFT coefficients

Is there any approximate relation in FFT coefficients?

For example, consider time domain signal $x_n$. Its $N$ point (assume $N$ to be even) DFT is given as $X_0,X_1,...,X_{N-1}$

Can I say something about the nature of $abs(X_1)/abs(X_0)$? I am trying to see the variation in DFT coeffcients and for that I thught one can sonsider the ratio of successive coefficients. My motivation is to see how similar the magnitude spectrogram at frequency $f1$ is to spectrogram at frequency $f1+1$ and $f1-1$

I tried to simplify the expanded equation but got stuck after a step -

$abs(X_0) = \Sigma_0^{N-1} x_n$

$abs(X_1) = abs(x_0+x_{N/2}+2(x_1.e^{-j.2\pi/N} + x_2.e^{-j.2\pi.2/N}+..+x_{N/2-1}.e^{-j.2\pi.(N/2-1)/N}))$

How do I (approximately) simplify $abs(X_1)/abs(X_0)$?