Transmitter devices and transmission methods transmit a modulated GMSK- or EDGE-signal in a transmission system, wherein normally the pulse shaping follows the given rules of standards for these mobile radio systems. The amount of TX spectra in the adjacent TX channels is predetermined by these rules. A second filtering step is suggested to be introduced for attenuating predetermined unwanted spectra in the adjacent transmit channels. A second goal of this suggestion is to reduce spectra at adjacent TX channels also at cases of nonlinearity at the TX Power Amplifier of the RF transmitter. Nothing must be changed in standards of mobile communication systems, for example GSM.