  We theoretically investigate the influence of designed pulse sequences in
restoring quantum coherence lost due to background noise in superconducting
qubits. We consider both 1/f noise and Random Telegraph Noise, and show that
the qubit coherence time can be substantially enhanced by carefully engineered
pulse sequences. Conversely, the time dependence of qubit coherence under
external pulse sequences could be used as a spectroscopic tool for extracting
the noise mechanisms in superconducting qubits, i.e. by using Uhrig's pulse
sequence one can obtain information about moments of the spectral density of
noise. We also study the effect of pulse sequences on the evolution of the
qubit affected by a strongly coupled fluctuator, and show that the non-Gaussian
features in decoherence are suppressed by the application of pulses.
