In telecommunication, attack time is the time between (a) the instant that a signal at the input of a device or circuit exceeds the activation threshold of the device or circuit and (b) the instant that the device or circuit reacts in a specified manner, or to a specified degree, to the input. Attack time occurs in devices such as clippers, peak limiters, compressors, and voxes.
Source: from Federal Standard 1037C
See also: Fall time.