Re: Looking for Linear Stretch Constant for 1D Function
- From: "jan hauben" <jan.hauben@xxxxxxxxxx>
- Date: Thu, 14 Jul 2005 21:30:29 GMT
>> if there is a lot of noise differentiation is NOT the way to go
>> high frequency compounds have large derivatives
>
> I don't think the noise is high frequency. It is probably more like
> drift although it's second derivative may be high. That is certainly a
> good point that you raise.
if there is a constant drift, the real function f_r(t) is something like
f_r(t) = f(t) + r*t + O(1)
f_r'(t) = f'(t) + r
f_r''(t) = f''(t)
the second derivative is identical to the one without the drift
if the noise is this kind, use the differential equation
>> or solve the integrated equation
>> k^2*g(k*t) + k^3*g'(0) + k^2*g''(0) = f(t) + f'(0) + f''(0)
>
> Should that not be g(k*t) + k*g'(0) + k^2*g''(0) = f(t) + f'(0) +
> f''(0) ?
exually it is
g(k*t) - k*g'(0)*t - g(0) = f(t) - f'(0)*t - f(0)
because
int(0 -> t, f'(k*t)*dt) = (f(k*t) - f(0))/k
sorry for the stupid mistake
.
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