Extended Phase-Shift Keying (EPSK) is a new digital phase modulation scheme that extends standard Phase-Shift Keying (PSK) to allow for phase shifts that exceed the traditional 2 pi limit. The new modulation can be applied to binary (BPSK), quadrature (QPSK), and m-nary PSK allowing the addition of symbols without requiring a decrease in the distance between symbols. The optimum bit-error rate BER for a band-limited PSK modulated system with typical practical constraints is shown to occur for a modulation factor of approximately 1.25, meaning that EPSK with phase-shifts of approximately 2.5 pi are required to achieve this optimum. We show that the hardware for both the modulator and demodulator can be very simple for this optimized EPSK, but to achieve the full benefit of EPSK it is necessary to develop a digital signal processor that removes the effects of "clicks" that occur under the conditions of low signal-to-noise ratio. Design of a high-quality Click Removal Signal Processor (CRSP) turns out to be the most critical issue for the practical implementation of EPSK.

The baseband filtering of digital data waveforms is considerably simplified by the use of superposition based filtering. This paper develops such a superposition based FIR filter from direct FIR filter structures. The resulting superposition FIR (SFIR) filter is shown to have no multipliers and only one adder, a significant simplification.

A novel digital filter structure is used to implement a digital finite impulse response (FIR) filter when the input is constrained to a two level non return to zero (NRZ) binary signal such as is common in digital communications systems such as digital cellular telephones. Depending on the specified filter, the structure superposes the impulse or rectangular pulse response of the filter for each bit in the NRZ signal. The superpositioning filter can be designed in either a parallel or serial configuration. The serial configuration results in the smallest hardware usage and is the preferred way of implementing the filter for minimum hardware low-power applications. A filter designed with the serial configuration will require only one summing point and no coefficient multipliers. Because there are no multipliers, this filter structure becomes very attractive for the implementation of FIR filters, when the input is a two level NRZ signal.

By expressing the frequency response of a Nyquist filter as a convolution of two functions, the mathematical complexity required to find the impulse response of the filter is reduced. Moreover, more efficient Nyquist filters than the popular Raised Cosine filter (i.e. wider 3 dB bandwidth, same absolute bandwidth, and shorter or same length impulse response) are generated by using well known Window functions such as Ramming and Blackman