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We present a novel method for the synthesis of complex fiber Bragg gratings (FBGs) which is based on an impedance reconstruction layer aggregation technique. The method takes as a starting point the accurate approximation of the sinusoidal perturbation (uniform or nonuniform) of the refractive index by local step functions by means of an inverse Fourier series relationship. This reduces the otherwise continuous scattering to only two points per local period and thus, the maximum spatial resolution as limited by the Nyquist criterion is achieved and there is no need to lump various periods of the FBG into an equivalent mirror. The main advantage brought by the method is the possibility of synthesizing structures containing defects or discontinuities of the size of the local period, a feature which yields different results with priorly reported methods to which the one reported here can be considered as complementary. In addition, this enhanced spatial resolution allows the synthesis of very strong FBG devices providing convergent solutions. We illustrate this fact by demonstrating the synthesis of a flat-top filter with a maximum reflectivity of 99.999%. The method renders directly the refractive index profile n(z) as it does not rely on the coupled mode theory since the grating is reconstructed using a V-I matrix formulation. The method is simple and its complexity is equivalent to those previously reported in the literature. Examples are given which prove that perfect reconstruction is achieved in both simple and complex grating profiles. Although a layer aggregation is presented here, the layer peeling (i.e., moving time frame) version of this algorithm is straightforward.