# Questions tagged [finite-differences]

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### finding the coefficients of the following difference equation so that it holds true

I'm having trouble solving the following problem: Find the coefficients $a_1,a_2,a_3$ so that the signal $x[n] = Ar^n \sin(\Omega_0 n)u[n]$, $|r|<1$, satisfies the following difference equation for ...
• 139
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### 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 ...
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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, ...
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 ...
• 11
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### Undo finite difference with arbitrary timesteps

I'm wondering if there is a way to undo a finite difference filter with arbitrary timesteps. In the simplest case of a two-sample finite difference of a time-series $x[n]$, y[n] = x[n]...
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I'm trying to implement the complex differentiation discriminator which is taken from Software-Defined Radio Using MATLAB, Simulink, and the RTL-SDR. The final result is $$s(t) = \frac{s_q'(t) s_i(t) -... • 726 0 votes 0 answers 22 views ### Square pulse test of Upwind Finite Differences I`m analyzing the numerical methods for the 1D convection equation for stability, consistency, and accuracy. I want to see How does this square pulse move in domain and time? Here is my code % ... 1 vote 1 answer 1k views ### Particular Solution to Difference Equation I have a system given by$$y[n] - \frac{1}{4} y[n-1] - \frac{1}{8} y[n-2] =3x[n] $$I want to solve for y[n] for x[n]=(\frac{1}{2})^nu[n]. The complementary solution evaluates to [k_1(\frac{1}{2})... • 211 5 votes 1 answer 809 views ### Compute the Second Order Derivative of Digital Image with Finite Differences I was looking for how to compute second order derivative of an image and came across the question kernels to Compute Second Order Derivative of Digital Image. In the top voted answer, it gives an ... • 53 0 votes 1 answer 79 views ### How to solve this Laplace integral for an averaging function in an iterative numerical (finite difference) model? I am trying to implement a mathematical model for vibrational damping described in this article. They provide an equation for damping force (F) as a function of: a spring constant (k) a damping ... • 533 0 votes 0 answers 28 views ### 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 ... • 101 3 votes 2 answers 483 views ### Multiplying the imaginary part of DFT with a linear ramp to get a derivative I am trying to understand the statement in a relatively old publication from 1970s, when Fourier transforms found applications in chemical analysis. The author quotes the derivative theorem citing ... • 584 1 vote 1 answer 478 views ### Different type of padding in image? I want to implement a gradient operator on an image in Matlab. Should I have to pad the image before its implementation? How do I decide which padding to use e.g. whether to use zero-padding or ... 1 vote 1 answer 134 views ### Numerical differentiation on circular data I have multiple time series of position data (x, y, z) and orientation data expressed as Euler/Tait-Bryan angles (yaw, pitch, roll) obtained from a head tracking device. I need to obtain velocity ... 1 vote 1 answer 95 views ### Calculate the Derivative of Gradient Field of an Image I meet a confusing thing in image processing recently.... Assume the image x \in \mathbb{R}^n, with its derivative (difference) matrix: D^+ = \begin{bmatrix} D_h \\ Dv \end{bmatrix} \in \mathbb{R}... • 273 1 vote 0 answers 95 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 ... • 155 0 votes 1 answer 370 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 ... • 141 2 votes 1 answer 75 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 ... • 123 3 votes 1 answer 169 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 ... • 129 2 votes 2 answers 434 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 ... • 83 0 votes 1 answer 688 views ### Using Parks-Mcclellan (or others) for FIR differentiator? I have never seen the use of Parks-Mcclellan for differentiator - most uses tend to be lowpass filters. Is this because Parks-Mcclellan implementation of FIR differentiator has numerical problems and ... • 83 1 vote 0 answers 79 views ### 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 ... 2 votes 1 answer 984 views ### Backward finite difference differentiation filter frequency response As title says what would be frequency response of backward finite difference differential filter, or what would be error of this differential filter, analyzed upon frequency of a signal? 5 votes 3 answers 816 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) $$If we ... • 423 3 votes 1 answer 404 views ### The Gradient Operator of a Vectorized Image in Matrix Form I have this optimization problem:$$ \arg \min_{ X \left( i, j \right) } \sum_{i, j} \left\| X \left( i, j \right) - 255 \right\|_{2}^{2} + \lambda \sum_{i, j} \left\| \nabla X \left( i, j \right) - \...
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 ...