Questions tagged [system-identification]

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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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1answer
40 views

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 ...
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23 views

Parametric vs Nonparametric system identification [closed]

Can somebody tell the main advantage and disadvantages of parametric and non-parametric system identification methods to each other? And why we use the parametric method in spite of their heavy ...
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14 views

SISO real data from any channel/system/process

I am looking for the dataset of single input - single output of any channel/system/process . I want a dataset that looks like this matlab sample data : dryer2 load dryer2; it is SISO with u1 and ...
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1answer
48 views

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-...
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10 views

How to calculate auto-covariance for a discrete-time symmetric block-wave?

I am newbie to this field, so this question seems difficult to me. I'd appreciate your help. For a discrete-time symmetric block-wave u(t), ...
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2answers
81 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, ...
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59 views

System identification with limited bandwidth

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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1answer
71 views

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 ...
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1answer
76 views

Why is White Noise so important in System Identification or Adaptive Filters

I'm looking to implement a feedback cancellation filter using Wiener Filtering, where an adaptive Wiener filter is used to cancel the feedback occurring in the path between a loudspeaker and a mic (...
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2answers
67 views

time invariance concept?

First of all ,please let me know?Is cosine time invariant or time variant? If latter is the case then if a time varying input like cos is given to a time invariant system,how will it behave? I have a ...
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1answer
98 views

Cost function for LTI system identification

I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions. The general approach ...
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3answers
227 views

Causal unstable system turn into stable anticausal?

I would appreciate it very much if someone would be able to provide some clarity, help or comment on this problem. I have been reading several papers on time series identification such as https://www....
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3answers
348 views

Protect an IIR filter from being reverse-engineered

I created a somewhat unique IIR filter and I want to protect the filter from being reverse-engineered I think you all know it is quite easy to get all the different weights of an IIR by using impulse ...
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1answer
102 views

Active Noise cancellation for non periodic signals

I observed that the coded algorithm for active noise cancellation is not able to cancel some of the signals like a human voice. Is there any solution for this? Can we really cancel non-periodic ...
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1answer
104 views

Implementation of Block LMS

In the implementation of block LMS, i need one clarification. In the 3rd step as shown in the figure attached, the summation over a product of input, $\mathbf{u}$ and error, $e$, associated with each ...
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58 views

system identification: MATLAB tfestimate gives different results for different Fs

So I have an experimental data; A is a chirp signal (sweep sine wave) and B is the response of the system. I identify the system as follows in MATLAB: ...
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1k views

Check if the system is linear

The system: $$ T(x[n]) = ax[n] + bx[n-3] $$ For me it seems that the system is linear: $$ \begin{align} T(\alpha_1x_1[n]+\alpha_2x_2[n]) & = a(\alpha_1x_1[n]+\alpha_2x_2[n]) + b(\alpha_1x_1[n-...
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2answers
791 views

Determine whether the system is linear?

$T(x[n]) = ax[n] + b$ $ T(\alpha_{1}x_{1}[n] + \alpha_{2}x_{2}[n]) = \alpha_{1}ax_{1}[n]+ \alpha_{2}ax_{2} [n] +b $ $ \alpha_{1}T(x_{1}[n] ) + \alpha_{2}T(x_{2}[n]) = \alpha_{1}(ax[n]+b) + \alpha_{...
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2answers
2k views

Difference between causality and memorylessness

I have found the particular definitions. Causality means that the output of the system does not depend on future inputs, but only on past input. Memory-less - does not depend on previous values of ...
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1answer
94 views

MIT exercise 6.003 HW2 - Concept of system initially at rest

I am following the MIT open course you can find here. My question is about one of the exercises given as homework in the latter and more specifically I think I am missing something on the concept of "...
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1answer
172 views

Find filter coefficients to model a device using its measurement

I am trying to realize a digital filter that has the same freq. response of an existing speaker. I have fed an audio sine sweep to the speaker and measured the speaker output, both at 48kHz. Then I ...
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1answer
32 views

Optimising an input signal for a system to minimise distortion of output signal

I have a discrete time-series signal which I am able to process before passing it through a system which distorts said signal. This system cannot be altered and is non-linear, but a signal can be ...
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0answers
67 views

Black-box system identification procedure

I am fairly new to system identification (some background in DSP), and I am trying to use a linear black-box system identification procedure. I am specifically looking for recommendations of sources ...
2
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1answer
585 views

Python toolboxes for state-space estimation via subspace estimation

Is there (open-source) toolboxes for state-space estimation via subspace estimation in Python? I know this is used in Matlab's n4sid function, but I didn't found any Python's implementation (even in ...
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3answers
117 views

Least Squares with blocks/updates

I have a continuous-time system that I want to fit via least squares. I just send $N$ digital samples $x[n]$ through the system and receive (via analog signal chain, ADC etc) $N$ digital samples $y[n]$...
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3answers
158 views

Causality as applied to capacitors

This question stems from a point of confusion that I still have about the causality, linearity, and time-invariance in LCCDEs. I wanted to use the capacitor as an example. Consider a capacitor with ...
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2answers
325 views

Is $y[n]=x[n] * x[n^2]$ invertible?

Is the following system invertible or not? $$y[n]=x[n] * x[n^2]$$ where $*$ stands for the aperiodic convolution operator. I have not been able to find a mathematically sufficient argument for it...
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2answers
316 views

Is it possible to estimate variance of noise for a step answer signal?

I know there is not possible to find the true noise of a measured signal. The only way to "find" the noise is to estimate the noise. Noise has the mean 0, but the variance varies. So assume that we ...
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1answer
183 views

What is the difference equation or system function of this system?

I am having trouble figuring out what the difference equation or the system function for this system is? Here ''R'' represents the unit delay. The fact that the delay is not part of the feedback loop ...
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1answer
224 views

Model validation after estimation — system identification — help with an example in Matlab

QUESTION: I want to determine how well the estimated model fits to the future new data. How do I validate the estimated model...what is the procedure? After system identification, how to do model ...
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1answer
261 views

What is the significance of a spike like autocorrelation function

I have some questions and doubts to which the answers are difficult to extract from text books. Hence I have posted this question here. Help would be extremely beneficial. Thank you. (1) The ...
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1answer
324 views

Estimate a Transfer Function from ARX Models vs. ARIMAX?

There is diffrent models which can be used to create a dynamical model by using least squares. Those models are following: ARX ARMAX ARIMAX OE BJ But if my goal with creating a dynamical model is to ...
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1answer
1k views

What is $H_2$ and $H_{\infty}$ control? [closed]

I can create a Linear Quadratic Gaussian Integral(LQGI) controller very easy by using GNU Octave. LQGI is in the area of Optimal Control Theory. But there is something called Robust Control Theory. ...
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2answers
424 views

Why use cross-spectral density to calculate frequency response?

I am taking a class about system identification and currently learning about cross-spectral density. My textbook says that the frequency response, G, of a system can be determined as $$G=\frac{S_{uy}}...
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1answer
308 views

Recursive system

Trying to identify if the system below is recursive or not, I would think a recursive system present output value would depend of a past output and not on a present output value. Is $$Y[n] = X[n] - ...
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1answer
611 views

Estimate transfer function from Bode curve

I have measured the magnitude response Y_mag(f) and phase response Y_phase(f) of an unknown physical system. Is it possible to ...
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33 views

Frequency identification as a convex problem

Suppose I have two time series, $x(t)$ and $y(t)$: $x$ is the output of a sine wave generator, and $y$ is the generator's frequency setting. Given a training set of $(x, y)$ pairs, Is it possible to ...
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1answer
139 views

Is there a way to determine the quality of an impulse-response relationship?

I'm new to system ID so be gentle. I have a modeled signal of streamflow that I would like to map to an observed signal of stream height. This lends itself nicely to a simple impulse-response kind of ...
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1answer
2k views

Check the stability of the system, $y[n]=u[n]$ [closed]

How do I check the following system $$ y[n]=u[n] $$ is BIBO stable or not ? $u[n]$ is the unit step function My Attempt: For the BIBO stability, the necessary and sufficient condition is $$\sum_{n=-...
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2answers
93 views

Modelling an existing DSP filter by analysing the differences between its inputs and outputs

A DSP filter produces always the same output. $$\boxed{\textrm{wav file}}{\longrightarrow}\boxed{\textrm{DSP}}{\longrightarrow}\boxed{\textrm{wav file(modified)}}$$ The DSP is a black box as I don't ...
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2answers
506 views

matched filtering in GSM

After the estimation of channel impulse response (using the training sequence in burst), to cancel the effect of channel on the received signal, I think, we should convolve the received signal with ...
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1answer
70 views

Help in problem formulation for estimation of image as a feature vector - SISO or MIMO FIR channel model?

Based on the paper Blind Image deconvolution: A feature vector is a list of numbers used to represent an image. The feature vector for my case takes values as symbols $-1,1$. An instance or an ...
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0answers
70 views

Why is the term deconvolution used more for signals and not so much (or at all) for systems?

Wikipedia defines mathematical deconvolution here, and with the examples given and my experience, what I've read over the years is that deconvolution is used to determine an input signal provided a ...
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2answers
963 views

The frequency response function (FRF) fails to detect the antiresonance of a system

I am trying to identify a vibrational systems by computing the frequency response function (FRF) of the system when a chirp signal is applied to its input. After comparing the FRF computed and the ...
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1answer
55 views

How to validate an estimated model in case of output-only data (in frequency domain)?

Before moving to the actual question, I would like to emphasize on the following points (maybe they are obvious to some of you, but I still would like to list them, since they make the difference): ...
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2answers
77 views

Proving conditions for controllability

Let's say I have the following LTI system: $$\dot{x}(t) = \mathbf{A} x(t) + \mathbf{B} u(t)$$ I need to somehow show the following is true or false (proof): This system is controllable if and only ...
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1answer
112 views

Showing a system is always controllable?

I need to show that the following system is always controllable: \begin{align}A &= \begin{bmatrix} -\alpha_1I_{k\times k}& -\alpha_2I_{k\times k}& \cdots &-\alpha_{n-1}I_{k\times k}&...
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2answers
347 views

Normalize data for transfer function determination?

I have the input and the output of a system and I want to determine the transfer function of it. I am using Ident Tool from Matlab. How is it more ok: to normalize the output and the input between 0 ...
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2answers
134 views

Memorylessness of simple delay system

As usual, $y(t)$ is the output signal of a system, and $x(t)$ is the input signal. I'm wondering whether or not a certain system has memory. It's easy for me to see that the system $y(t) = \int_{t-...