How to measure a shocking line?

... do you mean "shakes"? I have no idea what you're asking

>>8268644
>I have no idea what you're asking
How can I measure whether a line shocks for some period of time (not just a single big jump).
Consider the case where the line is made of discrete points.

>>8268684
Do you mean noise? But to answer your question maybe a Fourier transformation can work out

>>8268330
let's say you know every f(x) at a given x then you get the derivative (due limits) and if the derivative is much lower or higher than the derivative you got before it "shaking"

>>8269041
*it is

>>8268330
Calculate the variance of the derivative?

>>8268330
Take derivatives and find f'=0
Take Fourier transform and measure high frequency components in a window

>>8269041
>>8269952
>>8269962
He sad he's got discrete points

>>8270038
discrete Fourier transforms and MVT

>>8269962
>>8270042
Fourier can be false-positive in a sense that a function can have high frequency components despite being extremely smooth

>>8270061
Wavelets maybe?

>>8268330
I think the answer here is to count the total variance of an angle of a tangent line.

>>8270068
Is e^x smooth? Yes. But look at this:
http://www.wolframalpha.com/input/?i=integral+-pi..pi+e^x+*+sin+%2815x%29+dx
or even this
http://www.wolframalpha.com/input/?i=integral+-pi..pi+e^x+*+sin+%28150x%29+dx

Pretty sad that seeing e^x'th fourier coefficients you might think that it's shaky as fuck.

>>8270076
So the answer for the discrete case is this:
Sum 1..n-2 [arcsin(f'(i+1)/(1+f'(i+1)^2))-arcsin(f'(i)/(1+f'(i)^2))],
where f'(i) = (y(i+1)-y(i)) / (x(i+1)-x(i)).
This counts the total angle change for the tangent line.

>>8270084
I was thinking more of wavelets that aren't windowed sine waves, like https://en.wikipedia.org/wiki/Daubechies_wavelet , these seem to be better at detecting discontinuities.

>is there a method measuring how much a lin trembles
But you haven't even defined what you consider trembling.
I might give you an algorithm and you may just reject it says "that's not the kind of shaking I mean".
For example, you picture happens to display only random fluctuations that go in the opposite direction at every step.
If I go from 3 to 4 and then to 7, that's also soe sort of "trembling" but according to your examples.
If this zic zak captures what you mean, then you could just count the jumps, and that'll do, maybe weigthed by they jump size.

>>8268330
If you know beforehand what smooth function your "line" is supposed to look like (e.g. exponential, inverse, log, quadratic, etc) then you can model it as some function plus some random noise, determine the most likely parameters for the function, and then investigate the noise part that's left over. You can look at the support of this noise function (where it is nonzero), its magnitude, its variance, whatever you need.

If you don't know what function your line is supposed to be, then there's the unfortunate fact that even under the assumption the function it deviates from is smooth, you can approximate piecewise-continuous functions by smooth ones arbitrarily well, so you'll have to start by at least understanding in what ways can your line "tremble" and deviate from whatever function it should be.

Basically you can probably throw a mixture of Fourier and statistics at this problem.

>>8268330
>Is it continuous and differentiable
It does not shock.

>Is it continuous but not differentiable
It shocks a little.

>Is it not continuous and not differentiable
It shocks a fucking lot my nigga.