Questions tagged [discretization]
The discretization tag has no usage guidance.
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s to z domain transformation
I have $2^{nd}$ order bessel filter transfer function. I want to model this analog bessel filter in FPGA. For this I need its digital or discrete form. I am trying to get digital filter's coefficients ...
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Difference between simple 1st order low-pass filter equations
While reading about 1st order low pass discrete implementations I found out, the following 2 equations achieve similar results, but apparently not identical, but I thought they had the same origin. ...
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how is the formula of Xss in the numerical method for MATLAB derived?
On pages 193 and 194 of the book 'Control of Power Electronic Converters with Microgrid Applications' by Arindam Ghosh and Firuz Zare (the section can be viewed here), the author derived the steady-...
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How to compensate phase delay introduced by the digital integrator?
Let's say I have a digital integrator with transfer function in following form
$$
\frac{Y(z)}{U(z)} = \frac{T}{2}\cdot\frac{z + 1}{z - 1}
$$
I have been looking for a mechanism how to compensate the ...
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How is a discretized 1D signal be considered a 'vector'?
This question is perhaps related to the semantics or jargon of signal processing. I have checked plenty of advanced books/monographs on multivariable calculus and signal processing but could find an ...
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Behaviour of difference equation does not match that of its z-domain transfer function
I have obtained the following z-domain transfer function:
$\frac{Y(z)}{U(z)}=\frac{3.3641×10^{-7}×z^{6}+1.5584×10^{-5}×z^{5}+6.7263×10^{-5}×z^{4}+
5.5016×10^{-5}×z^{3}+8.525×10^{-6}×z^{2}+1.2303×10^{-...
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How to discretize the continuous time domain state space model?
I have a dsp algorithm which is based on the below given state space model in the continuous-time domain
$$
\begin{bmatrix}
\frac{\mathrm{d}\hat{\psi}_{r_{\alpha}}}{\mathrm{d}t} \\
\frac{\mathrm{d}\...
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Simulation of the discrete linear Kalman filter
I have been working on a Scilab simulation of the discrete Kalman filter which is used as a state observer of the
linear dynamic system. The Scilab script for the discrete Kalman filter is as follows
<...
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How to set initial values of the elements in the covariance matrices in the Kalman filter?
Let's say I would like to use the discrete version of the Kalman filter in a role of a state observer of a linear dynamic system. The observed continuous time domain dynamic system can be described ...
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Z domain transfer function including time delay to difference equation
How can get the difference equation of a $\mathcal{Z}$-transform transfer function with time delay? How does a time delay influence the difference equation?
For example:
$$H(z) = \frac{8z^{94}}{z-0.9}...
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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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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 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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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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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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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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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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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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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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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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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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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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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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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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