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I am developing a Game Boy emulator and I need to get a formula for generating pulse waves, like this:

enter image description here (picture from this Wikipedia page)

I know that it is possible to generate a square wave with this formula: $$f(x) = A (-1)^{\lfloor 2 (x - x0) / T \rfloor}$$

What formula could I use to get a pulse wave?

zdimension
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1 Answers1

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You can generate your picture using: $$\frac{x}{T} - \left\lfloor\frac{x}{T}\right\rfloor < \frac{\tau}{T}$$ where $<$ is a two-argument function that gives $1$ when true and $0$ when false, as is common in programming languages like C. The left hand side is the phase in $[0..1)$.

(Note when implementing on a computer it's best to accumulate the phase with wrapping, to avoid floating point precision issues that will be noticeable after a few minutes with 32bit float.)

Claude
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