Improved Nyquist filter with an ideal piece-wise rectangular characteristic

The present approach is centered on the optimization of a piece-wise rectangular transfer characteristic in order to obtain a minimal value of the error probability when the impulse response is sampled with small timing errors. We proposed a new parametric method for the design of the Nyquist filter using constraints in the frequency characteristic construction. We studied the family of new Nyquist filters based on a composite frequency characteristic and investigated its performances in terms of ISI error probability. This method of construction allows us to derive improved Nyquist filters in terms of ISI error probability. We also observed the variation of the side lobes of the pulses when a larger number of parameters is introduced in the proposed filter frequency characteristic. An implementation example of a real filter with improved performance in terms of ISI error probability when sampled with small timing errors is presented.