We consider pump-probe frequency integrated fluorescence signals. These transients, in general, arise from wave packets where the intrinsic dynamics and the response to the pump pulse is entangled in a complicated way. The signal from an infinitely short delta-pump pulse is the only exception. However, if the pump-probe signal is integrated over the frequencies of the pump laser, the signal can be expressed as a convolution of the pulse envelope with the signal obtained from a delta-pulse excitation. We consider the deconvolution of the pulse envelope and demonstrate that the signal corresponding to a delta-pump pulse can be recovered exactly from signals using pump pulses of finite temporal width. Numerical examples are presented for asymptotic fragment detection in the reaction, ICN --> I+CN.