A new approach to optimum pulse shaping in sampled systems using time-domain filtering

A new approach to time-domain pulse shaping in digital sampled systems is described. The proposed method allows time-limited impulse responses with optimum specified energy distribution in the frequency domain to be generated. Additional constraints to guarantee zero intersymbol interference are easily taken into account. Nyquist-type pulses which have the maximum possible amount of their total energy concentrated below some given frequency are one particularly important application. An example of such an impulse response with only 6 percent excess bandwidth is presented which shows that 99.96 percent of the energy can be concentrated in the desired bandwidth with a pulse 16 baud intervals long that can be generated using a read-only memory (ROM) with only 256 bits of storage. This new class of signals can be used advantageously for waveform generation and processing in digital data systems.