Consider a signal function of time in the form:
$\displaystyle t=0:0.005:10$
$\displaystyle y=(2sin(2 \pi t)exp(-0.1t)+0.2cos(20 \pi t)) / (4-0.1t+0.2sin(10 \pi t))$
How to derive two times the signal y?
I found the 1st derivative:
y | 0 | 0.005 | 10
f(t) | 0.05 | 0.0503 | 0.2271
Newton interpolation:
$\displaystyle F[x_0 , x_1] = \frac{f(x_1)-f(x_0)}{x_1 - x_0} = 0.06$
$\displaystyle F[x_0,x_1,x_2] = -4.231x10^{-3}$
$\displaystyle p(x) = f(x_0)+(x-x_0)F[x_0,x_1]+(x-x_0)(x-x_1)F[x_0,x_1,x_2]$
$\displaystyle p(x) = -4.231x10^{-3}x^2 + 0.06021x + 0.05$
$\displaystyle f'(t) = p'(x)$
$\displaystyle f'(t) = 8.462x10^{-3}x + 0.06021$
Is correct ?
For the second derivative I need to interpolate again?