To reflect advantages of continuous phase modulation (CPM), the invention provides a low complexity transmitter and receiver to transmit and receive CPM signals and 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 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.