Questions tagged [system-identification]

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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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1answer
82 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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2answers
894 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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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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573 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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1answer
31 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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1answer
235 views

Issues in generating AR model with a constraint

I am new to the topic of system identification and looking for a large Autoregressive (AR) model. Can anybody point out a large stable AR model which has more than 2 coefficients AND there should be a ...
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1answer
132 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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47 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
91 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
288 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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54 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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1answer
60 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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5k views

System identification packages

I've been hunting around for an alternative to Matlab's System Identification Toolbox, but the commonality of the terms "system" and "identification" are confounding the search. Are there any ...
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2answers
55 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
467 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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1answer
77 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
127 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
333 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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42 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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3answers
901 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
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
73 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
124 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
282 views

Confusion about 'memoryless' meaning

I am reading the book "Multiple input describng functions and nonlinear system design" written by A.Gelb and W.E.Vander Velde. At some point it says: Single-valued characteristics are termed ...
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55 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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3answers
133 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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3answers
105 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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2answers
194 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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2answers
292 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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1answer
163 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
787 views

Comparing multiple $\tt armax$ models

I would like to create an algorithm that, given an iddata, estimates different armax models with different ...
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1answer
195 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 ...
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1answer
217 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
241 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
849 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
392 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
291 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
549 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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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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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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2answers
126 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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2answers
71 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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2answers
92 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
477 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
287 views

Identification of the system with zeros

I need to identify two systems. Those are their Unit Step responses: I don't know, what order of the system that is. It could be second order system with zero in 0. Lecturer told me it was third ...
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1answer
3k views

is $F(x,n)=x(-n + 2)$ time invariant?

My book with answers to proakis and manolakis book says that $F(x,n)=x(-n + 2)$ is time invariant while my calculation shows that it is time variant. I have repeated them many times and I am mostly ...
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324 views

Equivalence of FFT and PSD based output based on the Frequency Response Function

Correct me please if I am wrong... I have just started working in the domain of signal processing using the Fourier Transform ($\mathbf{FFT}$) and Power Spectral Density ($\mathbf{PSD}$). I am trying ...
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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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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 ...