Design of linear phase matched filters with a causal real symmetric Nyquist pulse

Real symmetric pulse transmission under a linear phase condition is formally presented. The delayed raised-cosine pulse is considered, and a novel design method used to generate a Nyquist pulse with a linear phase polynomial for the denominator of the transfer function and an appropriate placing of the zeros of the numerator is described. The combination of even symmetry of the time response, and jo-axis transmission zero pairs leads to a linear phase pulse shaping filter which is its own match. Various aspects of the linear phase design method are investigated, using least-mean-square (LMS) timing error and the jitter performance of the pulse as figures of merit. A pulse symmetry factor is also defined and used. The maximum number of finite transmission zero pairs which guarantees zero pulse amplitude at t = 0 is derived, and the generated pulse has negligible energy outside the main lobe and better jitter performance than the standard raised-cosine spectrum pulse. The design method is flexible, and computationally robust. The transmission zero pairs on the jo-axis enable filter implementation in terms of ladder LC networks, with high stop-band attenuation and low component sensitivity. The causal real symmetric pulse method is extended to the discrete time domain and the discrete-time raised-cosine pulse. The transmission zeros of the discrete-time raised-cosine pulse are finite. Consequently the transfer function of the shaping filter is no longer an approximation, but is exactly obtained from the z-transform of the pulse, and the discrete-time raised-cosine is perfectly reconstructed as the unit-sample response of the filter. FIR filters for various values of the delay parameter are described.