# Questions tagged [system-identification]

System identification means building a mathematical model of the input-output relationship of a system by observing its inputs and the subsequent outputs.

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### Impulse response aquired by ifft seems to require circshift

On the system below: I have found W by inputing 20-1000 frequency and found amplitude and phase for each frequency. I've tested for minimum phase and none min S. But the answer is not logical for me. ...
50 views

### Generate a continuous time system with desired bode diagram

I have a fluid mechanics model that is heavy to simulate. Its main output is a scalar $q$ related to some energy transfer, and its input is a pressure $P$. This model, noted system 2, is coupled with ...
42 views

### How to represent nonuniform resampling of signal using math functions?

I am working on optical coherence tomography algorithm. In main pipeline I should use nonuniform resampling to eliminate transformation of optical signal in IR-spectrometer (that signal disperses by ...
208 views

### Get the inverse transfer function from the measured response

What is a numerically stable way to obtain the inverse transfer function from a measured response? I have a system that shows a low-pass behavior. I would like to increase the bandwidth by some form ...
1 vote
160 views

### Why time invariant system in order to know any output for any input using the impulse response?

Suppose we have a system $S$.We give it the input $\delta(t)$ and get a response $S(\delta(t))$.If the system is linear and time invariant we can calculate every output $y(t)$ from any input $x(t)$ by ...
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### Where to start in Nonlinear System Identification

Now that I have accomplished learning and applying various linear system identification techniques to simulated data sets. I am looking now to dig deeper into the world of system identification by ...
150 views

### Request for publicly available datasets for linear system identification practice

Apologies if the question is not fit properly here. Goal: I have a system identification project where I need a dataset to construct a dynamic model and perform correlation and/or predictions. The ...
122 views

### Is the system $y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$ invertible? [duplicate]

I have the following system: $$y\left(t\right)=\int _{t^3-1}^{t^3}x\left(s\right)ds\:$$ I was told to determine if it's invertible system, casual system, memoryless system and linear system. I was ...
1 vote
237 views

### The definition of Time Invariant systems

according to the wikipedia Time-invariant system article: Mathematically speaking, "time-invariance" of a system is the following property:: p. 50  Mathematically speaking, "time-...
185 views

### Does the error in the impulse response accumulate when applying a step-input?

Consider the model of the form $y[n]=0.9y[n-1]+x[n]+e[n]$, I forgot if this is called an ARX model but who cares, anyways assume $e[n]$ is a zero-mean white noise. I am applying a non-parametric ...
123 views

### Sufficient condition for a system to have memory

This is for a black box system which is not LTI and for which we have no input output expression, but we have some examples of sample inputs and corresponding outputs. I believe in this situation, we ...
1 vote
134 views

### IIR System Identification Difficult Problem

Identifying IIR systems is considered a difficult problem and different approaches have been proposed. Why is it considered difficult? I would like to find an accessible discussion of the problem (a ...
286 views

### How to design fir filter from transfer function

Transfer function is this equation in frequency domain: $$G(f) = \frac{1}{4\pi d} e^{i2 \pi d f/c}$$ or Hankel function d : constant (distance), c : 340 We may think we know complex number of ...
81 views

### Best way convert transfer function to FIR filter without group delay if i have complex transfer function data

when i calculate acoustic transfer function, system identification using adaptive fir filtering is usually used and that have not tap/2 group delay maybe. in simulation if i have complex number of ...
1 vote
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### Identifying system to represent output data as combination of 3 input data

I have some numerical data, which has 3 input vectors and 1 output vector. I have to use all the inputs to represent the output. I am new to dsp and struggling to understand how to do this. X1: Mostly ...
721 views

### Check whether a system has memory or not

My question is whether the systems below are memoryless or not: $1.) \ y(t)=K$ where $K$ is a constant $2.) \ y(t) = x(t_0)$ where $t_0$ is a constant So, from the definition I have been using so far ...
996 views

### What is the difference between a causal system and a system with memory?

As far as I know, memoryless systems are causal systems. But why aren't systems with memory necessarily causal? Since the system with memory is affected by past input and current input, I think that ...
73 views

### Design of digital filter with desired phase response

I want to design a digital filter with the following phase response in MATLAB. i.e. at 1kHz, the phase response should be 9 degrees, at 2khz phase response should be 18 degrees ,at 3kHz phase response ...
1 vote
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### Estimation of Group Delay from Noisy Frequency Response Measurements

Consider a linear, time-invariant system. Noisy measurements of the magnitude and phase associated with the frequency response of the system are available over some dense generally non-uniform grid ...
1 vote
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### How to find the perfect regularization number?

I have an issue! Assume that we are going to solve $Ax=b$ but $x$ contains noise.To minimize that noise we can use regularization: $$x = (A^TA + \lambda I)^{-1}A^Tb$$ Where $\lambda$ is a small ...
350 views

### Why does this transfer function estimation not work? System identification

Goal: I have an unknow dynmical system $G(s)$ and I want to find it from measurement data, output $y(t)$ and input $u(t)$. The data is frequency responses. Method: I begun first with creating the ...
1 vote
150 views

### Confusion regarding application of time invariance to flip system?

I am reading book signal processing first Chapter 5 I am reading article of time invariance Where author mentions example of a flip system as shown in attached photo ,i have drawn a red curve above ...
306 views

### Characterizing an unknown LTI system

What are the best approaches to characterize an unknown discrete time LTI system? I believe one of the approaches is to input a known input and measure the output to find a transfer function. What are ...
254 views

### Why is the error between the desired signal and estimated signal in the case of LMS filter remaining constant even after n number of iterations

I am giving white noise as input to an adaptive filter which is initialized to zero (value of filter coefficients of adaptive filter is 0). I am getting a desired response $d(n)$ by passing white ...
338 views

### Stabilizing the inverse transform of a system

Currently I am trying to understand an unknown mechatronic system. I used white noise as an input signal and measured the output of the system. Then I estimated a second order SISO transfer function (...
1 vote
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### Confusion about systems involving integrals

$$y_1(t)=\int_a^tx(τ)dτ$$ $$y_2(t)=\int_a^bx(t)dt$$ I'm confused about what are the input signals in each of these systems. To my understanding, in the second case the input signal is $x$ since both ...
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### Unstable plant transfer function identification

I would like to find the transfer function of an unknown unstable SISO plant. If it was a stable plant, I would input a sine sweep and measure the frequency response at the output; but I cannot do ...
1 vote
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### Neural networks in system identification - What type of activation functions?

I made a free software for all operative systems, even Android. It's called Deeplearning2C. It can train a neural network and generate C code and MATLAB-code. C-code for embedded systems and MATLAB-...
305 views

### As of 2019, which discrete nonlinear, time-invariant systems with memory are considered "easy" to model and identify?

There are several types of discrete nonlinear time-invariant systems with memory ("NTIM") which are considered "easy" to model and identify. Any such system can be represented using a Volterra series, ...
335 views

### System Identification with a Limited Bandwidth Input Signal and Region of Interest

Given a FIR filter $h[n]$. Its action can described as: $$\mathbf{y} = \mathbf{H} \mathbf{x} \\ \mathbf{y} = \mathbf{X} \mathbf{h}$$ where $\mathbf{H}$ and $\mathbf{X}$ is a Toeplitz matrix. If $h$...
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### Does $y[n] = x[n] \star (u[n]-u[n-2])$ have memory or is it memoryless?

$y[n] = x[n] \star (u[n]-u[n-2])$, by its definition is has to be a system with memory since it is depended from a fraction of time in the past, but if we calculate the difference $u[n]-u[n-2]$, it ...