# Questions tagged [discretization]

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6 votes
2 answers
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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 ...
• 163
5 votes
3 answers
854 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 ...
• 3,735
4 votes
3 answers
242 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 ...
• 77
4 votes
2 answers
108 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?
• 41
4 votes
1 answer
464 views

### 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 ...
3 votes
3 answers
5k views

### 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. ...
3 votes
1 answer
4k views

### 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-...
• 380
2 votes
2 answers
161 views

### 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 ...
• 599
2 votes
2 answers
373 views

### 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 ...
• 1,059
2 votes
1 answer
78 views

### 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 <...
• 375
2 votes
0 answers
17 views

### 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-...
• 131
1 vote
1 answer
1k views

### 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" ...
• 375
1 vote
2 answers
679 views

### 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 ...
1 vote
1 answer
231 views

### 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 ...
• 13
1 vote
2 answers
218 views

### 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 ...
• 11
1 vote
1 answer
596 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 ...
• 13
0 votes
2 answers
83 views