In some applications where the input signal is a burst signal, or the amplitude changes dramatically, the rise/fall time of the leaky integrator needs to be evaluated. The rise time can be derived from its step response; the fall time can be derived from its response with the initial conditions. The following formulas show how to calculate the rise and fall times, respectively:
- h[n] = 1 - αn+1
- h[n] = αn+1
α = 1 - 1/2λ
Considering when the output of leaky integrator achieves the 90% of final value for rise time calculation, which is around 1 dB lower than final value.
For the fall time, 1% (-40 dB) is used as which will illustrate a full-scale signal fall down to -40 dBFS, this makes the fall time is around double of rising time.
The following table shows rise/fall time for reference based on different time constants:
|Time Constant||Rise Time (0 to 90%)||Fall Time (1 to 1%)||Unit|