# Tagged Questions

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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)&...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
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. ...
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)?
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 ...
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 ...
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 ...
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) ...
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 ...
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 ...
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 ...
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 ...
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 (...
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 ...
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 ...
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 ...
1k views

### How is aicbic or other matlab function used to find the AR order of specific data?

let us consider following matlab code ...
454 views

### ARMA models for non stationary signals

let us suppose that we have non stationary signal,whose value is given by ...
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 ...
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 ...
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 ...
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 ...
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 ...
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 ...
3k views

### What are Autoregressive Coefficients?

Can anyone explain what are Autoregressive Coefficients? What is their meaning that is. Consider a method: ...
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 ...
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?
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 ...
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 ...