In actual standards, like LTE, WLAN, DVB-T etc. the transmission scheme Orthogonal Frequency Division Multiplexing (OFDM) is used to combat multi path fading. To prevent the impact of intersymbol interference (ISI) due to channel influence OFDM often uses a guard interval with a cyclic property (cyclic prefix (CP), therefore the name CP-OFDM). This leads to an easy and efficient implementation of the equalizer as an one tab equalizer per sub-carrier is often implemented. OFDM is designed to be an orthogonal scheme, which is in fact only valid without the presence of the channel, e.g. due to Doppler spread. Another possible scheme, which introduce other filter shapes than in CP-OFDM is a general filter-bank multi-carrier system, like in [1], [2], [3] and [4]. This schemes introduce Inter-Carrier Interference (ICI) due to the non-orthogonal impulse shapes of each sub-carrier.  This work focuses on the design and the analysis of a linear equalizer in a general filter-bank multi-carrier system to reduce the impact of the interference introduced by using non-orthogonal schemes. For that, a comprehensive study on linear equalizer and GFDM systems should be done to get an overview on the possible solutions. A good channel model should be found, which includes the impact of doubly dispersive channels. By using this channel model an equalizer should be designed, first by assuming perfect channel state information (CSI).