We study the effect of ultrachirped pulses on the population inversion of two-level atoms. Ultrachirped pulses are defined as those for which the frequency chirp is of the order of the transition frequency of the two-level atom. When the chirp is large enough, the resonance may be crossed twice, for positive and negative frequencies. In fact the decomposition of the field into amplitude and phase factors, and the corresponding definition of the instantaneous frequency, are not unique. The interaction pictures for different decomposition are strictly equivalent, but only as long as approximations are not applied. The domain of validity of the formal rotating wave approximation is dramatically enhanced by a suitable choice, the so-called analytic signal representation.