Graduate Non-sinusoidal waveform model

[P3dr0]

Hi, I am a ninth-grade student from Portugal with nothing to do, and I have decided that I want to build a simple regression algorithm in Desmos (the online calculator) to fit random binary inputs and maybe predict the next binary digits (although that part may take a considerable amount of time). For now, I am just trying to find a way to create non-sinusoidal waves, but I can't find any model for it. Can anybody tell me a simple yet effective model for what I am trying to achieve?
PS: I have created an algorithm based on Fourier's theorem, but it doesn't work quite well. (I'll attach a photo and a link of what I have done.) This is the simplest version I have created so far, but I have tried other parameters. However, when I add more elements (more parameters), the function becomes noisier.

Link: https://www.desmos.com/calculator/h3nww18l8p

 

[FactChecker]

What you have done is perfectly correct, but I am not sure that it is a good example of what you want to do. Notice that your example is perfectly linear with a slope of 1 and very near the (x=0, y=0) origin. The sin() function is also very linear with a slope of 1 near the origin. The tiny value of $b$ means that the inputs of sin() will be very close to 0 and the large value of $a$ means that the slope will be close to 1. If $a=1/b$, the slope would be exactly 1 at the origin.

 

[berkeman]

Welcome to PF.

to fit random binary inputs and maybe predict the next binary digits

If the inputs are random, how can you do any predictions for future digits?