In modern wireless communication systems, such as satellite communications and wireless networks, the need for higher data rates without the need for additional transmit power has made Continuous Phase Modulation (CPM) one of the most attractive modulation schemes in band limited channels. However, as the data rates keep increasing, the spectral width of the CPM signal increases beyond the channel bandwidth and performance becomes constrained by the intersymbol interference (ISI) that results from band-limiting filters. We propose two approaches to the problem of equalization of band-limited CPM signals. First, our efforts are focused on shortening the channel impulse response so that we can use a low complexity MLSE equalizer. We implement the channel truncation structure by Falconer and Magee and adapt it to work with CPM signals. This structure uses a, a more derivable, pre-filter to shape the overall response of the channel, so that its impulse response is of shorter duration. Simulation results show that near-MLSE performance can be obtained while dramatically reducing MLSE equalizer complexity. In our second approach, we focus on eliminating the group-delay variations inside the channel passband using an FIR pre-filter. We assume the channel to be time-invariant and provide a method to design an FIR filter so that -when convolved with the band limiting filter - it results in more constant group-delay over the filter passband. Results show that eliminating the group-delay variations in the band limiting filter passband reduce the amount of ISI and improve bit error rate performance. / Master of Science