How to create a rectangle wave (duty cycle $\ne$ 50 %)?

Question

I'm trying to use phase-shifted SquareWave[] functions to create a rectangle wave:

SquareWave[{0, 1}, x/100] * SquareWave[{0, 1}, x/100 - offsetx]

Two things:

1. This only allows for duty cycles less than 50 %.
2. While it's handy (it's always the phase shift $0\dots 1$, regardless of horizontal scale), I'm confused that offsetx isn't a function of the x scaling

Is there a general function to create rectangle waves with duty cycles from 0 % to 100 %?

Answer 1

See if this helps

squareWave[t_, period_, duty_] := UnitBox[Mod[t/period, 1.]/(2. duty)]

Plot[squareWave[t, 10, 0.8], {t, -2, 21}]

Answer 2

What I'd do:

With[{d = 1/3}, (* duty cycle *)
 Plot[(1 + (-1)^Floor[x] (-1)^Floor[d - x])/2, {x, -5, 5}, 
  Axes -> {False, True}, Frame -> True, PlotPoints -> 105, 
  PlotRange -> {-5/4, 5/4}]]

If you absolutely must use the SquareWave[] function, there is the identity

$$\text{SquareWave}[\{a,b\},x]=\frac{a+b}{2}+\frac{b-a}{2}(-1)^{\lfloor 2 x\rfloor}$$

I'll leave the conversion up to you.