  One approach to maintaining phase coherence of qubits through dynamical
decoupling consists of applying a sequence of Hahn spin-echo pulses. Recent
studies have shown that, in certain noise environments, judicious choice of the
delay times between these pulses can greatly improve the suppression of phase
errors compared to traditional approaches. By enforcing a simple analytical
condition, we obtain sets of dynamical decoupling sequences that are designed
for optimized noise filtration and are spectrum-independent up to a single
scaling factor set by the coherence time of the system. We demonstrate the
efficacy of these sequences in suppressing phase errors through measurements on
a model qubit system, $^{9}$Be$^{+}$ ions in a Penning trap. Our combined
theoretical and experimental studies show that in high-frequency-dominated
noise environments this approach may suppress phase errors orders of magnitude
more efficiently than comparable techniques can.
