In this letter we proposed the linear combination of two ISI-free pulses with different decay rates in order to obtain a new Nyquist pulse. The proposed pulse contains a new design parameter β, giving an additional degree of freedom to minimize the bit error probability performance in the presence of symbol-timing errors, for a given roll-off factor α. Several practical tools are implemented for evaluating the performance of the proposed filter. The novel pulse is evaluated in terms of the bit error probability performance in the presence of symbol-timing errors. Eye diagrams are presented to visually assess the vulnerability of the transmission system to ISI, and the maximum distortion is estimated as a quantitative measure of performance.

A K-exponential filter is derived and utilized for pulse shaping to reduce peak to average power ratio (PAPR) without intersymbol interference (ISI). While keeping the same bandwidth, the frequency responses of the filters vary with different values of the parameter k. The minimum PAPR is associated with a value of the parameter k when the roll-off factor α is specified. Simulations show that the PAPR can be reduced compared with the raised cosine (RC) filter in various systems. The derived pulse shaping filters also provide better performance in PAPR reduction compared with the existing filters.