# Questions tagged [finite-differences]

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### Not getting the same step response from Laplace transform and it's respective difference equation

I am trying to simulate a plant on a microcontroller. The transfer function of the plant is $$G_{p} \left( s \right) = \frac{2}{\left( s + 3 \right) \left( s - 1 \right)} \tag{1} \label{1}$$ The step ...
• 11
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### Is non-causal, non-LTI solution to difference equation correct?

Find a solution to the difference equation $y[n]-\frac{5}{6}y[n-1]+\frac{1}{6}y[n-2]=\frac{1}{3}x[n-1]$ that is neither casual nor LTI, where $y[0]=y[1]=1$ and $x[n]=\delta[n]$ The homogenous ...
• 155
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### How far can numerical differentiation be accurate for sinusoids?

Suppose you have samples of uniform interval of a sinusoidal signal that is some sum of sinusoids. Forget about aliasing, as the signal is bandlimited. If we have infinite number of samples at ...
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### Derivation of 9 point Laplacian filter

I'm reading a paper on how construct isotropic laplacian filter, and perhaps because it's an old paper, the notation in it really bothers me a lot. So can someone please explain it to me? For example, ...
### Numerical computation of the derivative of a curve valued in $\operatorname{Diff}(\mathbb{R}^2)$
Assume we have a (discretized) sufficiently smooth curve $\alpha : [0, 1] \to \operatorname{Diff}(\mathbb{R}^2)$. Further assume that this curve is generated via a large deformation diffeomorphic ...