This thesis presents the results of research in the area of digital demodulation of FM signals. The first part of the thesis describes the performance of digital Hilbert-transformers and Differentiators that are optimized in a determined bandwidth. These digital filters are used to build a digital Klapper-Kratt detector. According to this procedure, the coefficients of the digital Klapper-Kratt detectors up to the filter length N=25 are calculated and the resulting discriminator ripple computed and evaluated. One suggested algorithm gives the opportunity to balance the detector at a certain center-frequency. The major part of this thesis describes a new approach towards the digital FM-demodulation. This approach uses an FIR-linear filter as a frequency discriminator. The structure of the discriminator has no restrictions as to certain lengths or certain kinds of symmetry of coefficients. A practical approach to the FIR discriminator is given and the chosen approximation technique is described. The dependence of FIR-discriminator length, optimized bandwidth and resulting discriminator ripple is presented. Weighted and split weighting functions are described with discriminator examples. Changes in the desired weighting function can be used to shape the resulting discriminator ripple in a desired way. Discriminators with these additional design criteria are presented. Finally the results of the new design is discussed and a comparison and evaluation given.