# Questions tagged [finite-differences]

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1 vote
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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 ...
1 vote
453 views

### How to calculate a 3D Fourier Transform?

I am currently employing a centered finite difference method to simulate the excitation of a circular membrane by a forcing term in Python, and the code is functioning as intended. To further enhance ...
75 views

### 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, ...
1 vote
996 views

1 vote
93 views

### 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 ...
789 views

### Discrete State Space Model - Why Are We Calculating $x \left[ k + 1 \right]$ Instead of $\dot{\boldsymbol{x}} \left( t \right)$?

A continuous state space model is defined as follows. $$\dot{\boldsymbol{x}}(t) = A \boldsymbol{x}(t)+ B \boldsymbol{u}(t) \\ \boldsymbol{y}(t)= C \boldsymbol{x}(t)+ D \boldsymbol{u}(t)$$ If we ...
365 views

### Time invariance and linearity of recursive system

I am confused about the definition of linearity and time invariance of recursive system Given $$y[n] = y[n-1] - y[n-2] - x[n]$$ To test time invariance, we shift the input $x[n]$ for shifting and ...
645 views

### Causal Noise Free 1st Order Derivative in Discrete Domain

I need to have causal noise free first order derivation (Derivative). Now I am using a simple finite differences formula: $$\frac{ x \left( n \right) - x \left( n - 1 \right) }{ {T}_{s} }$$ The ...
73 views

### Understanding the resulting image matrix when differentiating image

Let $A$ be a image matrix and let $P(i,j)$ be the gray level of pixel $i,j$. Let $0$ be black and $255$ be white Assume I want to differentiate this image with respect to the columns $(x)$ as in I ...
268 views

### Given a Horizontal Derivative Kernel What Would Be the Output Image?

Hi, im solving this problem and everything went well until i went and solved the position p(5,3) and i got the answer of 0. However, the solution guide lists the solution as 150 which is pointed at ...
168 views

### Linear Difference Equation and Method of Least Squares

I'm reading the book "Fault-Diagnosis Systems" by Isermann in the par. 9.2.1a. The author explains how to estimate the parameter of a linear difference equation using Least Squares. We start with a ...
418 views

### Frequency response of numerical differentiation by polynomial interpolation / finite difference

One can use polynomial interpolation (or finite difference) to do numerical differentiation. However, there seems to be a surprising lack of interest in obtaining frequency response of this numerical ...