CODEWITHSUNDEEP
functional-programmingwolfram-mathematicamathematical-optimizationdiscrete-mathematicscontinuous-fourier
lejin
lejin

Reputation: 98

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?

Upvotes: 1

Views: 356

Answers (1)

Chris Degnen
Chris Degnen

Reputation: 8655

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}]}]

enter image description here

With variation in the terms you can modify the response to follow a path such as shown below.

Ref: PID controller theory

enter image description here

There is also a relevant Mathematica demonstration: PID Control of a Tank Level

Upvotes: 1

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