Compensation of chromatic dispersion in modern communication systems is typically done by using FIR filters as part of digital signal processing.

They can be derived by starting from the well-known transfer function $$ H\left(f\right) = \text{exp}\left\{-\mathrm{j}\frac{\beta_2}{2}\left(2\pi f\right)^2\ell\right\},\;\;\; \beta_2 =- \frac{D_\mathrm{C}\lambda_0^2}{2\pi c_0T^2}\left(\approx -21.67\,\mathrm{ps}^2/\mathrm{km}\right) $$ and using the inverse Fourier transform to get the corresponding time domain representation. Changing the value for $D_\mathrm{C}$ to $\tilde{D}_\mathrm{C} = - D_\mathrm{C}$ and inserting this yields [1] in discrete time: $$ h\left(n\right) = \sqrt{\frac{\mathrm{j}}{4K\pi}} \text{exp}\left\{\mathrm{j}\frac{n^2}{4K}\right\},\;\;\;K=\frac{D_\mathrm{C}\lambda_0^2\ell}{4\pi c_0 T^2} $$ By only using a couple of taps, the so called truncated FIR filter is obtained.

Minimizing the error caused by the truncation gives the least-squares FIR [2]. By limiting the range where allpass characteristics are needed, the filter can be further improved (pulse-shaping aware).