Real-life application of sinc-in-time data or sinc(t) function?
I found that my customers' response time on an application is varying in a Sinc-in-time fashion. i.e. Sinc(t) across time. Can this information be applied to obtain any relevant system other than just for a fun observation?
Solution
If you customers' response is following a diminishing oscillatory response as plotted below, you could apply measurements to create a PID controller.
Plot[{2, -2 Sinc[x] + 2}, {x, 0, 6 Pi},
PlotRange -> {Automatic, {0, 3}},
PlotStyle -> {Dashed, Automatic},
Epilog -> {
Inset[Style["Initiation", 14], {3, 0.2}],
Inset[Style["Response", 14], {14, 2.2}]}]
With variation in the terms you can modify the response to follow a path such as shown below.
There is also a relevant Mathematica demonstration: PID Control of a Tank Level
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