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Periodic piecewise functions?

Posted 3 years ago
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How would one create a piecewise periodic function (without using recursions)?

For example I'd like to make this function Piecewise[{{x, 0 <= x <= Pi}, {x - 2 Pi, Pi < x < 2 Pi}}] repeat itself to infinity...

7 Replies

Something like this?

f[x_] := Switch[Mod[x, 2 Pi] <= Pi, True, 0, False, x - 2 Pi]

Plot[f[x], {x, -Pi, 4 Pi}, PlotStyle -> Thick]

enter image description here

Posted 3 years ago

This seems to be on the good track....

enter image description here

I don't want it to climb up the y-axis though... :/

But that is the expression you posted -- perhaps this?

f[x_] := Switch[Mod[x, 2 Pi] <= Pi, True, 0, False, Mod[x, 2 Pi] - Pi]

Plot[f[x], {x, -Pi, 4 Pi}, PlotStyle -> Thick]

enter image description here

Posted 3 years ago

Hint: Think Mod[x, 2 Pi]

That should be enough.

Posted 3 years ago

This gives the "sawtooth" wave: enter image description here

Which is not what i was hoping for.

That's what David had in mind

Clear[nPeriodic]
nPeriodic[x_?NumericQ] := 
  Piecewise[{{Mod[x, 2 Pi],         0 <= Mod[x, 2 Pi] <= Pi}, 
             {Mod[x, 2 Pi] - 2 Pi, Pi < Mod[x, 2 Pi] < 2 Pi}}]
Posted 4 months ago

....

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