Wavelet Packet based Multi-Carrier Modulation (WPMCM) offers an alternative to the well-established OFDM as an efficient multicarrier modulation technique. It has strong advantage of being generic transmission scheme whose actual characteristics can be widely customized to fulfill several requirements and constraints of advanced communication systems. In the last decades wavelets have been favorably applied in signal and image processing fields but they just recently attracted attention of the telecommunication community. Therefore, some research questions remain to be addressed before novel WPMCM can be used in practice. One of the major concerns involves the performance of WPMCM transceivers under various synchronization errors. In this thesis we analyze the interference in WPMCM transmission caused by the carrier frequency offset, phase noise and time synchronization errors. Using standard wavelets the sensitivity of WPMCM transceivers to these errors is evaluated through simulation studies and their performances are compared and contrasted to OFDM. New wavelets are designed to alleviate the WPMCMs vulnerability to synchronization errors. Consequently, a filter design framework is built that facilitates the development of new wavelet bases according to the specific demands. In this regard the expressions for Inter Carrier Interference (ICI) and Inter Symbol Interference (ISI) in WPMCM transmission are first derived and stated as a convex optimization problem. Then an optimal filter that best handles these deleterious effects is designed and developed by means of Semi Definite Programming (SDP). Through computer simulations the performance advantage of the newly designed filter over standard wavelet filters is proven and further its performance is compared to the conventional OFDM.