  Faster than Nyquist signaling increases the spectral efficiency of pulse
amplitude modulation by accepting intersymbol interference, where an equalizer
is needed at the receiver. Since the complexity of an optimal equalizer
increases exponentially with the number of the interfering symbols, practical
truncated equalizers assume shorter memory. The power of the resulting residual
interference depends on the transmit filter and limits the performance of
truncated equalizers. In this paper, we use numerical optimizations and the
prolate spheroidal wave functions to find optimal time-limited pulses that
achieve minimum residual interference. Compared to root raised cosine pulses,
the new pulses decrease the residual interference by an order of magnitude, for
example, a decrease by 32 dB is achieved for an equalizer that considers four
interfering symbols at 57% faster transmissions. As a proof of concept, for the
57% faster transmissions of binary symbols, we showed that using the new pulse
with a 4-state equalizer has better bit error rate performance compared to
using a root raised cosine pulse with a 128-state equalizer.
