To reflect advantages of continuous phase modulation (CPM), the invention provides a low complexity transmitter and receiver to transmit and receive CPM signals. CPM is a spectrum–efficient digital modulation scheme, which enables constant or quasi–constant envelope communication, leading to significant battery savings on top of bandwidth and energy savings. Despite the desirable properties of CPM, the complexity of an optimum CPM demodulator can be very high, due to the inherent memory nature of CPM. Specifically, the number of states in an optimum CPM demodulator is exponentially dependent on the length of the frequency pulse, L. The present invention addresses a significant reduction in the CPM demodulator complexity, and is especially well–suited for large values of L, e.g., L ≥ 3. The invention utilizes a linear filter front end as an integral part of the CPM demodulation process so as to reduce the ISI inherent in CPM transmit signal, and minimizes the influence of L in the reception process. To that end, the invention renders the complexity of a CPM demodulator non–exponentially dependent on L, and L only has a weak impact on the number of coefficients of the linear front end filters. Moreover, the invention provides a simple way of forming CPM signals for a digital communication transmitter using parallel Time Invariant Phase Encoders, which simplifies the production of CPM waveforms on software or hardware.