Time-domain design of frequency-sampling digital filters for pulse shaping using linear programming techniques

The use of time-domain specifications is demonstrated for designing frequency-sampling digital filters that generate data pulses for transmission over an ideal band-limited channel. Desired characteristics of the transmitted pulse are used to formulate the set of constraint equations and objective function used in linear programming to obtain an optimum set of filter coefficients, i.e., frequency samples
{| H(k) |}
- The constraints are the amplitudes assigned to the set of regularily spaced samples taken from the pulse. The objective function is either to minimize the maximum absolute error between desired and generated pulse samples over the specified pulse duration or to provide zero crossings in the transmitted pulse with near-zero slope in order to protect against intersymbol interference (ISI) due to timing error (jitter).