Signal Processing Stack Exchange
Signal Processing Stack Exchange

Questions tagged [discretization]

23 questions
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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 the image The first integrator is a forward Euler and the…
Ben
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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 scipy.signal exists, but I want to be able to change the cutoff frequency (smoothly) at…
fabian789
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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 uniqueness of this representation of the analog signal to…
HYMD
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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 implemented on a DSP which reads in the digitize…
FaradayParadox
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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?
Joseph
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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…
Matthias La
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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 from unit-amplitude additive white Gaussian noise…
Jason S
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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. img_color = imread('photo.jpg'); img_gray = rgb2gray(img_color); imshow(img_gray); [rows, cols] =…
flamingo_stark
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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 I just went by intuition and converted it to…
Pier-Yves Lessard
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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 stated in some places, for example in the Matlab…
PidTuner
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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" approximation of the form: $y[k+1] = e^{-T/\tau} y[k] +…
rhz
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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 understand is why the freq response of the resulting…
RMS
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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 expected. However the bode plot of the discrete…
Martin
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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}…
Steve
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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 $$\bar{\mathbf{x}}(k) = \mathbf{A}_d\cdot\hat{\mathbf{x}}(k-1) + \mathbf{B}_d\cdot \mathbf{u}(k-1)$$ $$\hat{\mathbf{x}}(k) =…
Steve
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