# Questions tagged [discretization]

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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 ...
40 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 ...
34 views

### 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 ...
27 views

### 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 $\mathbf{B}$, ...
150 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-...
39 views

### 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 ...
36 views

### 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 ...
135 views

### 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 ?
118 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 the ...
61 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 ...
91 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, ...
79 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 ...
### 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?