Questions tagged [discretization]

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Discretization method for a simple first order system

I know there are multiple ways of discretizing a continuous system. In many occasion, I needed a discrete model for a simple first order system (RC circuit, inertial load, etc.) and most of the times ...
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4 votes
2 answers
635 views

Implementing a Butterworth Filter Manually in C/C++ via Second Order Sections

Short background: I want to implement a lowpass butterworth filter in C/C++. The end goal is to use this in a low-latency Python program, for which of course ...
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How to choose appropriate discretization method for the state estimator?

Let's say I have following open loop state estimator of a dynamic system in the continuous time domain $$ \begin{bmatrix} \frac{\mathrm{d}\hat{\psi}_{r_\alpha}}{\mathrm{d}t} \\ \frac{\mathrm{d}\hat{\...
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1 answer
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How to check that the state observer works appropriately?

I have implemented a discrete state observer for a given dynamic system in continuous time domain in following form $$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \...
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States transformation of the bilinear transform

I have used the bilinear (or tustin) transform for a while, have been though the derivation of it and also through the concept of frequency warping. Something that I still not understand that is ...
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Discrete implementation of the PI controller

I have been implementing discrete PI controller in the incremental (velocity) form in C++. I have been looking for the anti-windup mechanism. One idea which I have can be described by following ...
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3 answers
171 views

Under what conditions is there a one-to-one mapping between continuous-time and discrete-time signals?

As the sampling theorem dictates that the uniform sampling frequency must be at least twice the maximum frequency present in the bandlimited signal (Nyquist rate), a question arises about the ...
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DFT Signal DFT Length N , FFT

If we sample a signal let say sine(2 * pi * f) with f=1Hz and a sampling Frequency of Fs = 8Hz, is it right that the length of the data should be N = Fs/f or multiple of Fs/f like N= d*(Fs/f) with d=...
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First Order Hold discrete-time approximation to first order continuous-time linear system

Consider the following first order linear system described by: $\tau \frac{d}{dt}y(t)=-y(t) + x(t)$. I have seen a discrete time approximation to this system using a "First Order Hold" ...
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1 vote
1 answer
259 views

Impulse Invariant method for digital filter design

One of the known methods for discretizing analog filters is impulse response invariant. We get the impulse response in time domain, discretize it and then get the Z transform. What I am trying to ...
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Discrete-time sampling of filtered white noise

I am trying to understand how I can relate a discrete-time random process to a continuous-time random process sampled at discrete times. Suppose I have a noise source $N_\tau(t)$ which is derived ...
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Discretize process noise in Kalman filter

Reading P. Andrews et al. I see that it is very common to do the following approximation of the process noise covariance matrix: $$Q_{k} = G_{k-1}QG_{k-1}^{T}\Delta t$$ so that the propagation ...
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Discretizing my continuous system in Matlab

I was hoping someone could help me with conducting my discretization in MATLAB. I have a linear system with known data: sampling interval $T$, system matrix $\mathbf{A}$, input matrix $\mathbf{B}$, ...
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1 answer
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Frequency prewarping of a bilinear transform (Tustin transform)

sadly I'm not too well aquinted with discretazation methods. At the moment I struggle to reproduce a bilinear transform with frequency prewarping. I have the following transfer function in the s-...
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Derive the Forward Euler substitution for transfer function

In the book "The control handbook. Volume 1 " by Levine, the author shows that the transfer function: can be aproximated and discretized in the transfer function: using the forwar euler ...
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1 answer
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Proof of Forward Euler for discretizing a transfer function

In Levine book "The control handbook" it is shown that, for discretizing a transfer function $\frac{1}{s}$ using Forward Euler i simply have to replace s with $\frac{z-1}{T}$. How can extend the ...
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1 answer
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Forward Euler Discretization

I don't understand why the substitution $s=\frac{z-1}{T}$ allows us to discretize a transfer function from laplace to z-transform through Forward Euler Discretization. Can you explain to me ?
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5 votes
3 answers
450 views

Frequency warping when integrators are replaced with backward-euler and forward-euler integration

Resonant controllers are used in the power industry. The transfer function is $G_{res}(s) = \frac{K_i s}{s^2 +2\omega_c s+ \omega_o^2}$ The "textbook" discrete implementation is depicted in ...
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4 votes
1 answer
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s-Domin or z-Domain - What to Use for Mixed systems

I recently had to deal with a power electronic system where I had to implement a dynamic model of a power converter in order to design a suitable controller for that converter. The control will be ...
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1 answer
749 views

Discretizing a Controller with the Backward Difference Method

In the book "Modern Control Engineering" by Paraskevopoulos it's proved how to discretize a generic controller in the form: $G(s)=\frac{Y(s)}{U(s)}=\frac{a}{s+a}$ where $a$ is a constant. Done this, ...
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2 answers
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Matlab - Bode plot of Lag Filter + Integrator

I am rather new to Matlab and I just cant make sense of what I see in the bode plot of the continuous and discrete version of the same function. The bode plot of the continuous function looks as ...
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3 votes
3 answers
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Reduce the Number of Intensity Levels of a Grayscale Image in MATLAB

I have written a Matlab script to reduce the number of intensity levels of each pixel of a grayscale image from 256 to some power of 2. ...
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5 votes
2 answers
91 views

Kalman Filter: Why $ Q $ Discrete Is Defined as $\int_0^Te^{\mathbf{A}\tau} Q e^{\mathbf{A}^T \tau} d\tau$?

I would like to ask, why in the transformation to the discretization, $\mathbf{Q}$ is obtained from the expression containing the integral (image attached), what is the theory behind it?
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