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Questions tagged [system-identification]

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1answer
24 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
42 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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0answers
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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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4answers
714 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
185 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_{...
4
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2answers
742 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
35 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
71 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
23 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 ...
2
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0answers
33 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 ...
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0answers
238 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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58 views

Estimation of the frequency response data using Matlab command invfreqz?

I would like to determine frequency response and then impulse response of the displacement equation (eq. 1 please see screen shot of the task below). In this example we study a response of the finite ...
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0answers
75 views

ACF and impulse response

These are questions according to the system identification. I can understand some questions: Is there a relation between autocorrelation function and impulse response? Is it possible to identify the ...
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0answers
32 views

Are the update equations for LMS in Real Time System Identification being handled correctly

Question: Are the Least Mean Squares (LMS) coefficient update equations and step size being handled correctly? Some background information: This algorithm is implemented on the ezdsp5535 on which ...
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3answers
97 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
102 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
140 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
44 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
100 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
201 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
180 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
210 views

Estimate a transfer function from ARX models - Is ARIMAX better?

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
485 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
265 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
240 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
430 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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0answers
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
119 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 ...
2
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1answer
926 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=-...
3
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2answers
85 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
409 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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0answers
68 views

System Identification and I/O delay

In the below picture I have a Multi Input Single Output model with A and B the inputs and O is the output. A flow of materials start from variable A then reaches variable B after 30 minutes and then ...
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0answers
65 views

How can I separate three noise sources?

This is the system I am trying to characterize I have three uncorrelated noise sources. I am trying to characterize all three noise sources, and more important find out what the original noise ...
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1answer
69 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
66 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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1answer
670 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 ...
1
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1answer
46 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
68 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
71 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
181 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 ...
0
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2answers
102 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-...
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0answers
29 views

What kind of reference signal would be preferable when identifying a closed loop process?

Given the following reference signals constant Gaussian white noise sequence a sequence of sinusoidal signals of different frequencies or a PRBS signal Which one would be preferable when trying to ...
2
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2answers
299 views

System identification only using sine input?

Recently, I'm working on modeling a sensor's system model using system identification. Subject to the experiment condition, I only have the sine input signal. In addition, the frequency can not ...
3
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1answer
186 views

System Identification with periodic signal confusion

I want to find the ETFE (Empirical Transfer Function Estimate) of the system $G(e^{j\omega})$: Where $H(e^{j\omega})$ is some filter that zero-mean white Gaussian noise $e(k)$ passes through. Let's ...
2
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1answer
3k views

Determining if a system involving integrals is time varying or time-invariant

I've been studying for a signals and systems class coming this fall and am trying to understand the following problem. $$$$ Show whether the following system is time invariant or time varying: $$S_1:y ...
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0answers
660 views

Matlab's invfreqs won't fit at low frequencies

I'm wondering of anyone can explain why invfreqs() is unable to fit a polynomial to the data in the image below. The red line is the measured frequency response of an analog system. I should mention ...
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0answers
191 views

Identifiability of a state space model (Dynamic Linear Model)

Take a general linear Gaussian state space model (SSM)(aka Dynamic Linear Model DLM): \begin{align} X_{t+1}&=FX_t + V_t\\ Y&=HX_t+W_t\\ V_t &\sim \mathcal N(0,Q)\\ W_t &\sim \...
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1answer
145 views

What is the estimator used in this paper for system identification?

Paper : System Identification using Symbolic Chaotic Sequence download link proposes EM-UKS estimator for system identification of a linear FIR channel when excited by non-linear input. In Fig 3 of ...
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1answer
184 views

Expectation maximization of moving average with binary source input

I am trying to do blind system identification of a univariate linear FIR model: I am unsure if the approach is correct or not and any help to further proceed with the maximization will be great. ...
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3answers
2k views

Sine sweep vs impulse response

What kind of pros and cons does these method for identifying a system have? I seem to have a hard time finding literature discussion in this issue. I am operating on a linear system, or the linear ...