Hi sci!
I'm a musician and i need a little help.
I need some functions of a real variable in R like tan^-1.
I need C0 class functions, I don't need an odd one, but it should have:
f(0) = 0
f(x) < 0 ∀ x
lim x-> +inf f(x) = 1
A nice feature could be:
f'(0) = 1
Thanks you so much!
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>f(0) = 0
>f(x) < 0 ∀ x
Uh.
>f(x) < 0 ∀ x
That's not how you use quantifiers (I know what you're trying to say, but that's not proper syntax).
>f(x) < 0 ∀ x
>lim x-> +inf f(x) = 1
What.
Also,
>f(0) = 0
>f(x) < 0 ∀ x
>f'(0) = 1
And >>>/sqt/
I'm so sorry, I meant f(x) < 1 ∀ x
But thinking it again, I just need a horizontal asymptote and f(x) < lim x-> +inf f(x)
I can normalize my result later
Try f(x) = a*arctan(b*x) for some appropriate constants a and b.
That's much easier. How about 1-e^(-(x^2)?
Upside down bell curve! Best function.
tanh(x)
f(x) = x / (abs(x) + c) should do the job for all positive c.
>bitches about syntax
>doesn't provide anything helpful about proper syntax
Kill yourself
So you know, OP, most people put their quantifies in front of their conditional statements and you should probably include a set. So say something more like "for all x in R, f(x)
tanh(x) is exactly what you need
This is the result, just a first try...
You can see the waveform of the original sine,atan, tanh, x / (abs(x) and 1-e^(-(x^2).
tanh is nice, but the Upside down bell curve is interesting. =)
Ty m8! XD
...
Making sound with help of math and programming?
I have the same hobby :D
Pic related, program I'm writing from scratch.
I'm more a musician than a programmer, I work with max/msp to make audio and video. This sketch is made for try with a simple compressor/waveshaper. The arctan give nice results for it's simplicity!
fourier series
It's not really a class of functions, but it sounds like you're interested in sigmoid functions OP. This is a bunch of functions that are generally S-shaped (like 1/tan x) and they're used a lot in machine learning and statistical stuff in general. There's a good list on wikipedia: en.wikipedia.org
> f(0) = 0
> f(x) < 0 for any x
You mean for any x except x = 0?
Can it be piecewise? Does it need to be continuous and differentiable at x = 0? You could do something like the following:
f(x) = {1 - 1/x, x > 1; 0, -1 < x < 1, 1 + 1/x, x < -1}.
Yep! I really like sigmoid curves!!! Thanks!!!
Whoops. fucked that one up. I meant the following:
f(x) = {1 - 1/x, x > 1; -(x^3) + x, -1 < x < 1, 1 + 1/x, x < -1}.
This way, you have f'(0) = 1, f(0) = 0, and f(x) < 1 for all real values of x. Finally, lim x -> +infinity of f(x) = 1. This is continuous (f(1) = 0 and f(-1) = 0) for all real values of x, but not differentiable for +/- 1.
Just use a synth and its ADSR desu, it's easier.
The erf function looks pretty good, especially because i can use it as a class of functions and change the graph in real time.
My problem is that it's a integral function! I know that i only need to find out a primitive of the integral part and and take the difference between F(0) and F(x), but the point is that I don't know hot to integrate that! I just have a high scool education in math, sorry.
I have tried with wolframalpha.com