  We study the performance of dynamical decoupling in suppressing decoherence
caused by soft-cutoff Gaussian noise, using short-time expansion of the noise
correlations and numerical optimization. For the noise with soft cutoff at high
frequencies, there exists no dynamical decoupling scheme to eliminate the
decoherence to arbitrary orders of the short time, regardless of the timing or
pulse shaping of the control under the population conserving condition. We
formulate the equations for optimizing pulse sequences that minimizes
decoherence up to the highest possible order of the short time for the noise
correlations with odd power terms in the short-time expansion. In particular,
we show that the Carr-Purcell-Meiboom-Gill sequence is optimal in short-time
limit for the noise correlations with a linear order term in the time
expansion.
