. Alternative definitions Other definitions of rise time, apart from the one given by the Federal Standard 1037C (1997, p. R-22) and its slight generalization given by , are occasionally used: these alternative definitions differ from the standard not only for the reference levels considered. For example, the time interval graphically corresponding to the intercept points of the tangent drawn through the 50% point of the step function response is occasionally used. Another definition, introduced by , uses concepts from statistics and probability theory. Considering a step response , he redefines the delay time as the first moment of its first derivative , i.e. Finally, he defines the rise time by using the second moment Rise time of model systems Notation All notations and assumptions required for the analysis are listed here. Following , we define as the percentage low value and the percentage high value respect to a reference value of the signal whose rise time is to be estimated. is the time at which the output of the system under analysis is at the of the steady-state value, while the one at which it is at the , both measured in seconds. is the rise time of the analysed system, measured in seconds. By definition, is the lower cutoff frequency (-3 dB point) of the analysed system, measured in hertz. is higher cutoff frequency (-3 dB point) of the analysed system, measured in hertz. is the impulse response of the analysed system in the time domain. is the frequency response of the analysed system in the frequency domain. The bandwidth is defined as and since the lower cutoff frequency is usually several decades lower than the higher cutoff frequency , All systems analyzed here have a frequency response which extends to (low-pass systems), thus exactly. For the sake of simplicity, all systems analysed in the "Simple examples of calculation of rise time" section are unity gain electrical networks, and all signals are thought as voltages: the input is a step function of volts, and this implies that is the damping ratio and is the natural frequency of a given second order system. Simple examples of calculation of rise time The aim of this section is the calculation of rise time of step response for some simple systems: Gaussian response system A system is said to have a Gaussian response if it is characterized by the following frequency response