Rising time is defined mathematically for the performance of a system for a unit step response. My research is in the human muscle control. In several trails, I measured the 90% rising time of the muscle reaction between two arbitrarily chosen points. Therefore, the rising time I obtained in each trail depends on the distance of start and target points which are different trail to trail. So, how can I compare the rising times of these trails? Is there any definition of Rising time that is decoupled from the distance between the start and target points? Something like non-dimensional rising-time?
Dear Mohsen,
I suggest you to see links and attached files in subject
- Auditory reaction time as a function of stimulus intensity ... - Springer Link
https://link.springer.com/content/pdf/10.3758/BF03329370.pdf
- On the ion transport system of photosynthesis - De Gruyter
https://www.degruyter.com/downloadpdf/.../znb-1968-0222.xml
Best regards
Hi Mohsen,
In order to compare the Rise Time of the signals in a meaningful way, the signals should be normalized by the given formula
snormal = (s − smin) / (ssteady − smin)
where
s = measured signal,
smin = minimum value of the measured signal,
ssteady = steady state value of the measured signal.
For example, the measured signals in Fig. 1 are given by:
sblue = 1 - (e^(-t/2) sin((sqrt(3) t)/2))/sqrt(3) - e^(-t/2) cos((sqrt(3) t)/2),
sred = e^(-t/2) (e^(t/2) - 0.34641 sin((sqrt(3) t)/2) - 0.8 cos((sqrt(3) t)/2)).
The normalized signals are plotted on Fig. 2.
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