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1
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1answer
31 views

How do I test stability of a MIMO system?

Let's say I have a system similar to two interconnected IIR filters described like this: \begin{align} x_1(t)&=a_{11} x_1(t-1)+a_{12} x_1(t-2) +a_{13} x_2(t-1) + a_{14} x_2(t-2)+y_1(t)\\ x_2(t)&...
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1answer
23 views

Different results for different orders of estimating AR model using Yule-Walker equations

I'm trying to use MATLAB to estimate the AR parameters to the following filter: $$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$ As I can see, the process at the output of this filter depends ...
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0answers
25 views

How can I estimate a signal similar to my data using ar modeling in matlab

To be more specific, I have a time series which corresponds to a section from an EEG signal. The idea is obtain AR coefficients and then use these coefficients to create a simulation where I can get a ...
0
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1answer
57 views

Determining the autocorrelation sequence from an AR model

I have the following equation: $$x(n)=\frac{14}{24}x(n-1)+\frac{9}{24}x(n-2)-\frac{1}{24}x(n-3)+w(n)$$ where, $w(n)$ is a stationary white noise process with variance $\sigma^2_w$ Now, I want to ...
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0answers
31 views

Autoregressive Model for EEG frequency analysis?

I want to do EEG frequency analysis in matlab using autoregressive models (e.g. Burg's method). How do I do this correctly? I just treated each channel individually (loop over channels), so I go ...
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0answers
36 views

Excite AR-Model with white noise to reconstruct a signal

The following Matlab code creates an AR process and then calls aryule to find the AR Model. Now, as far as I've read, you can excite this model with white noise and ...
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1answer
85 views

How can I reconstruct a Time series using it AR coefficients in MATLAB?

I have estimated AR coefficients of a time series using "aryule" function in MATLAB. Now I want to obtain the error of the estimated model. I think at first I must reconstruct it. so How can I ...
3
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1answer
108 views

Linear Prediction of AR Process

A discrete signal x is generated by the recursive process $$ x_n = x_{n-1} - 0.2 x_{n-2} + w_n $$ where $w_n$ is white noise with zero mean and unit variance. What is the optimum order of a linear ...
1
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1answer
197 views

Filtering a signal using Autoregressive (AR) filter and finding the coeff of AR filter using Yule Walker equation in MATLAB

I have a random signal x of 1000 samples and I've to generate y1 by filtering x using an ...
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0answers
23 views

LPC analysis without implicit windowing

In MATLAB, the documentation for the LPC function states: lpc uses the autocorrelation method of autoregressive (AR) modeling to find the filter coefficients. ...
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0answers
26 views

What is a “Unit Shock” in an Impulse Response Function?

Is a "one unit shock" in an impulse function of variable "temperature" a 1% increase or 1 more "unit" (1 degree)?
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1answer
84 views

AR model order selection for half second EEG fragments

I am using MATLAB to evaluate power spectral density estimates of half second EEG signals, using modified covariance method. Can anyone suggest me how to select the AR model order for this process? Is ...
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0answers
35 views

Comparing AR coefficients derived from different sampling rates

I'm interested in comparing the coefficients of AR processes computed from different dynamic texture videos. That is, $A_1$ and $A_2$ are the $d \times d$ coefficients for dynamic texture videos 1 and ...
2
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0answers
66 views

How to evaluate performance of an ARMA, MA or AR model?

How to evaluate performance of a model after estimating ARMA/MA/AR parameters for any process x(n)? How to regenerate back a process after estimating average parameters? what kind of performance ...
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0answers
44 views

how to find the distance of the root from the origin?

Good Day, I have 9 polynomial roots. i have plotted the roots. my problems are: 1)how to find the distance of the roots from origin? I want to find the distance of all the roots from the origin. 2) ...
0
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1answer
69 views

How to plot the root of polynomial in Matlab?

I obtained this polynomial equations: $$A(z) = 1 - 0.7987 z^{-1} - 0.125 z^{-2} - 0.511 z^{-3} + 0.06889 z^{-4} + 0.3465 z^{-5} + 0.4809 z^{-6} + 0.04951 z^{-7} - 0.5298 z^{-8} + 0.1828 z^{-9}$$ How ...
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0answers
119 views

How to determine the order from Auto-Regressive model in Matlab?

I have time series vibration signal recorded for 10 seconds. I segmented the vibration signal into a number of frames. I need to use an Auto-regressive model for this signal. AR model is used to ...
0
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1answer
47 views

Forecasting with ARMA models, from a filter point of view

ARMA models are afaik just filters with transfer function $ {MA(z) \over AR(z)} \equiv {FIR(z) \over IIR(z)} $ . However forecasters of stock prices, market trends ... seem to be mainly ...
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0answers
29 views

Yule walker equation limited matrix size

Definitions For an ARMA model $$x_n=-\sum_{p=1}^P a_px_{n-p}+\sum_{q=0}^Qb_qw_{n-q}$$ where $w_n$ is zero mean stationary white noise with unit variance. It is straightforward to show that the ...
1
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1answer
96 views

Conceptual question from signal processing: impulse response and AR coefficients

In continuation to the previous question Conceptual questions from signal processing I have a doubt which is: Consider an Autoregressive model (AR(2)): $$ y(t) = ay(t-1) + by(t-2) $$ and a FIR (...
0
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1answer
152 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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0answers
66 views

ACF and PACF Confidence Levels for ARMA

I'm trying to figure out where exactly to draw the confidence levels for the autocorrleation function (ACF) and the partial autocorrelation function (PACF) for an ARMA model. For PACF I found that a ...
2
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1answer
314 views

Can someone show the details of how to apply AIC for sinusoidal models to specific data?

NOTE: This is a question that another user has been trying (unsuccessfully) to ask. Because the multiple questions asking, essentially, the same thing have either been deleted by me (because they were ...
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0answers
1k views
0
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1answer
454 views

ARMA models for non stationary signals

let us suppose that we have non stationary signal,whose value is given by ...
0
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1answer
2k views

Convert normalized frequency to real frequency in AR model

Let us suppose that we have modeled signal using AR model, and suppose we have following model: I used spectral estimation function from MATLAB pyulear Now ...
0
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1answer
732 views

Power spectral density interpretation

After reading this question: PSD (Power spectral density) explanation I am still a little confused as to what extra information the PSD gives us over simply taking the magnitude of the fourier ...
1
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0answers
47 views

Is a Stationary VAR Process with Zero Mean Gaussian Innovations a Gaussian Stationary Process?

Consider the stationary VAR process $${\bf X}_t = \sum_{\tau = 1}^{L} A_\tau {\bf X}_{t-\tau} +{\bf \epsilon}_t$$ If the innovations $\epsilon_t \sim MVN({\bf 0},\Sigma)$ then is ${\bf X}_t$ a ...
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0answers
55 views

Fitting VAR Process with Generalised Gaussian Noise

Consider the $m$-dimensional VAR process $${\bf x}_t = \sum_{l=1}^{P} A_l{\bf x}_{t-l} + {\bf e}_t$$ where the componenets of ${\bf e}_t$ are spatially and temporally independent and follow a ...
2
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1answer
1k views

ARMA vs. AR and then what?

Sorry if this sounds elementary but I am struggling to grasp the physical idea behind ARMA (auto-regressive, moving average) process. The "AR" part is intuitive and so is "MA", but put together? If I ...
2
votes
1answer
81 views

Choosing inverse Z-transform equation, given that $|a|<1$

Given that $|a|<1$, then which of those inverse-Z-transform equations are we to use? I am leaning towards the first because (as I understand it), $z$ is merely a complex number that is ...
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2answers
3k views

What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: ...
5
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1answer
191 views

How to perform model fitting for system identification

I am having a really hard time in understanding how to formulate a model say linear AR model to represent a communication channel or maybe any motion. I have the experimental data representing the ...
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0answers
95 views

How to estimate an auto-regressive model?

Given a periodic impulse train and it's impulse response, how is an auto-regressive model of this system computed or estimated?
4
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2answers
2k views

Different state-space representations for Auto-Regression and Kalman filter

I see that there are different ways to write an AR model into a state-space representation, so that we can apply Kalman filter to estimate the signal. See Example 1, 2 and 3 here. I wonder what ...
5
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1answer
2k views

How to decide whether to use AR or MA for smoothing data?

Imagine I've got some offline data that I want to smooth. I could use an auto-regressive or moving-average filter of some appropriate order for conducting the smoothing. On which criteria should I ...
7
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1answer
335 views

Why does over-modelling an adaptive AR NLMS filter fix sharp spikes?

I just simulated an auto-regressive second-order model fueled by white noise and estimated the parameters with normalized least-mean-square filters of orders 1-4. As the first-order filter under-...
7
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2answers
199 views

What input to use for an AR model of a vowel sound?

I've recorded a 2-sec pronunciation of a vowel sound. The first 0.12 or so seconds of the signal are shown below. Now, I've constructed an auto-regressive (AR) 8th-order model to compress this signal....