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What's the formula for a smooth almost-ramp/sawtooth sine/cosine wave?


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I don't know what it's called but I'm trying to find a general formula a cosine function that's very similar to a regular cosine function except it's not symmetric about every local minimum, instead it's lopsided. It's like a sawtooth/ramp wave but it's not a triangle and it doesn't have vertical lines, it's just as if a sin(x) got squished on one side of every cycle. Like for any given cycle, it's really steep slope on one side, then after the maximu/minimum it's a really shallow and low slope until the next cycle.

Once again this site is horribly glitched and it's not even letting me post links anymore, so I guess the only picture I can relate it to is a chi distribution. Imagine a chi distribution that keeps repeating and that's basically the type of sine wave I'm trying to find a formula for.

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Sounds like you need a tool which will generate a Fourier transform froma drawing of a waveform (but I am not aware of any such tool!)

 

There is some relevant discussion here: http://mathematica.stackexchange.com/questions/38293/make-a-differentiable-smooth-sawtooth-waveform

 

And about halfway down this page: https://documentation.apple.com/en/logicexpress/instruments/index.html#chapter=A%26section=3%26tasks=true


And here: https://www.reddit.com/r/math/comments/28jdp3/formula_for_a_shited_sine_wavesmoothed_sawtooth/

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Not that you'd know but that's definitely not what I'm looking for, I' not looking for some little loophole to a perfect sawtooth wave, I'm looking for something that's completely different from a sawtooth wave but happens to coincidentally bear some geometric resemblance to it, I was only using sawtooth wave as an example of the general shape, I definitely wasn't looking for any sort of "exact" sawtooth wave. After doing some research, the only thing I can really say is that it has something to do with a relaxation oscillator or Van Der Pol Oscillator (wait only google chrome works for scienceforums???/scienceforums is sponsored by google (but wait doesn't that make it biased)????????????). Basically I want something that looks nearly like that relaxed van der pol but only in the form of y=f(x) and I don't know how to make it to grow steep first and then release gradually as opposed to how the waves look in the links which is that they gradually build up THEN release quickly/steeply.

Edited by MWresearch
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... (wait only google chrome works for scienceforums???/scienceforums is sponsored by google (but wait doesn't that make it biased)????????????). ...

 

Nope - I used Firefox for all my dealings with SF.n either via windows 10 or Linux depending where I am. A bit of empirical research might not go amiss in some posts before claiming an institutional bias. We do have adverts to defray expenses - but the site usage is not exclusive to Google Chrome

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Nope - I used Firefox for all my dealings with SF.n either via windows 10 or Linux depending where I am. A bit of empirical research might not go amiss in some posts before claiming an institutional bias. We do have adverts to defray expenses - but the site usage is not exclusive to Google Chrome

To be honest I have every right to be frustrated, after all the complaints of glitches they still won't even fix the most basic problems. But, let's not stray too far off topic.

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