on. Let us call Fo(a) the ideal Fourier transform of the impulse to be transmitted, SO that at the receiver it is compressed to completely eliminate the ISI. Input Output FIGURE 9.58 Block scheme of per channel optical pulse shaper used to compensate ISI. (After Jiang, Z. et al., Nat. Photon. 1, 463, 2009.) Next Generation Transmission Systems The waveform generator approximates Fo(a) with the following function (9.87) j=-v/2 where S is the global bandwidth GA represents the AWG response Aw is the step between two consecutive frequency samples, while the number of samples is equal to v+1. Imagining to realize the pulse shaper with an InP integrated circuit, is the process- caused intrinsic error in reproducing the complex numbers Fo(jAw). The potential performance of the precompensation method depends on the bandwidth and the number of samples at the AWG output, besides the precision with which the com- plex values Fo(jAw) are reproduced by the intensity and phase masks/modulators. In Figure 9.59, an example of the ability of a pulse shaper based on Gaussian AWGs is shown. In Figure 9.59a, the spectrum to be reproduced is shown, while in Figure 9.59b it is superimposed to the spectrum at the output of the shaper of Figure 9.58 that is assumed to be realized with 100 frequency slices and Gaussian AWGs. The simulation parameters are an optical bilateral bandwidth of 200GHz and typical tolerances for InP Mach-Zehnder Modulators that uses similar technology steps. Since the configuration above is quite near to an ideal shaper even with practical param- eters, it results that the main limitation to the compensation capability of this method is due to nonlinear effects. Fo(w) Maximum error out or the tails 22 2.5% FIGURE 9.59 Example of the shaper accuracy in reproducing a complex spectrum: (a) test spectrum to be reproduced; (b) comparison of the spectrum created by the shaper with the original spectrum; (c) particular of one of the spec- trum peaks where the maximum error is located if the tails far from the main spe