  We consider channels affected by intersymbol interference with
reduced-complexity, mutual information optimized, channel-shortening detection.
For such settings, we optimize the transmit filter, taking into consideration
the reduced receiver complexity constraint. As figure of merit, we consider the
achievable information rate of the entire system and with functional analysis,
we establish a general form of the optimal transmit filter, which can then be
optimized by standard numerical methods. As a corollary to our main result, we
obtain some insight of the behavior of the standard waterfilling algorithm for
intersymbol interference channels. With only some minor changes, the general
form we derive can be applied to multiple-input multiple-output channels with
intersymbol interference. To illuminate the practical use of our results, we
provide applications of our theoretical results by deriving the optimal shaping
pulse of a linear modulation transmitted over a bandlimited additive white
Gaussian noise channel which has possible applications in the
faster-than-Nyquist/time packing technique.
