  In this work, average Hamiltonian theory is used to study selective
excitation in a spin-1/2 system evolving under a series of small flip-angle
$\theta-$pulses $(\theta\ll 1)$ that are applied either periodically [which
corresponds to the DANTE pulse sequence] or aperiodically. First, an average
Hamiltonian description of the DANTE pulse sequence is developed; such a
description is determined to be valid either at or very far from the DANTE
resonance frequencies, which are simply integer multiples of the inverse of the
interpulse delay. For aperiodic excitation schemes where the interpulse delays
are chosen pseudorandomly, a single resonance can be selectively excited if the
$\theta$-pulses' phases are modulated in concert with the time delays. Such a
selective pulse is termed a pseudorandom-DANTE or p-DANTE sequence, and the
conditions in which an average Hamiltonian description of p-DANTE is found to
be similar to that found for the DANTE sequence. It is also shown that
averaging over different p-DANTE sequences that are selective for the same
resonance can help reduce excitations at frequencies away from the resonance
frequency, thereby improving the apparent selectivity of the p-DANTE sequences.
Finally, experimental demonstrations of p-DANTE sequences and comparisons with
theory are presented.
