Questions tagged [autoregressive-model]
The autoregressive-model tag has no usage guidance.
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1answer
40 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 ...
0
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0answers
36 views
Finding time-varying coefficients for a VAR model by using the Kalman Filter
I'm posting this again, since after my last post i've been able to advance the code quite alot. I'm still trying to write some code in R to reproduce the model i found in this article.
The idea is to ...
0
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1answer
29 views
How to characterize this whitening filter?
A little bit of background: I am interested in whitening in the least-square estimation.
In this sense, consider a univariate signal $y$. Assuming the covariance of $y$ is $\mathbf{A}\sigma^2$. ...
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0answers
25 views
Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT
Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal?
If I have a measured signal which has good ...
0
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1answer
54 views
Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
0
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1answer
32 views
AR Modeling: Why residual is white noise?
I was going through AR modeling.
The AR model of a covariance stationary process can be expressed as:
$$x[n]=\sum\limits_{i=1}^{p} \alpha_i x[n-i] + \epsilon[n]$$
where $p$ is the model order and $...
1
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0answers
176 views
Linear Predictive Coding example in MATLAB
I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process:
Encoding
Generate ...
1
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0answers
45 views
Understanding linear predictive coding in MATLAB
I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
1
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1answer
36 views
Explanation of Spectral Line Splitting when AR process is overmodeled
In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation
$$x(n) = 0.9x(n-...
1
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1answer
146 views
Simplest way to generate AR(2) process on MATLAB
As part of a project I need to use autocorrelation method of estimating model paramters of an autoregressive process on MATLAB.
Can anyone tell me the simplest way to generate an AR(2) process on ...
0
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1answer
56 views
ARMA & MA methods: how do you know the error terms?
Reading the ARMA model for the first time, and I'm confused.
Let's say I have a time series
x = [1, 2.1, 2.9, 3, 4.1]
According to the ARMA model, $X_t$ is a ...
1
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1answer
84 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 ...
2
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2answers
59 views
Finding the auto-correlation sequence $r_{xx}[k]$ for an AR(2) process
Consider the following recursive difference equation of a LTI system, where $v[n]$ is a white noise, zero-mean process with $\sigma_v^2 = 1$.
$
x[n] = v[n] + 0.75x[n-1]-0.25x[n-2]
$
I want to ...
2
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1answer
172 views
Linear Predictive coding vs AR modeling
I'm looking for a suitable explanation of the circumstances in which the LPC error polynomial for a discrete time process x[n] is replaceable with an error polynomial categorized under the AR model? I ...
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2answers
65 views
Difference Between Two Forms of Equations of Auto Regressive (AR) Model
I found equation 1 for Autoregressive model in various books and articles but i also found equation 2 for AR model, I understand the physical meaning of the equation but two different equations ...
0
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1answer
48 views
Find the coefficient of an AR-model
How can I infer the coefficients for an AR(2) model given an autocorrelation plot?
What I have tried so far: I can see this a cos-wave of 0.4 Hz, and then i find the values for each step $(1, 0.9211, ...
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2answers
40 views
Confusion regarding model order and lags
I have similar questions as the one asked in these posts: https://stackoverflow.com/questions/47083890/fir-filter-length-is-the-intercept-included-as-a-coefficient-matlab/47085339?noredirect=1#...
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1answer
907 views
How to generate colored Gaussian noise and adding it to a ODE system - Do I need Euler-Maruyama method?
In the tutorial, when white noise process is added to ordinary differential equations (ODE), the ODE becomes a stochastic process. Then the stochastic process needs to be solved using Euler Maruyama ...
0
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1answer
91 views
Autoregressive Exogenous model on multiple datasets in MATLAB
I had trouble translating this exact question into search queries, which is why I am turning to you. Any sources you can provide on the topic would be greatly appreciated.
Say your data contains ...
0
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1answer
322 views
Finding autocorrelation matrix of an autoregressive process AR(1)
Having that $\ v(n) = [x(n),x(n-1),x(n-2))]^T $, and being $\ x(n) $ an autoregressive process AR(1) with known variance $\ \sigma_v^2 $ and transfer function $\ H(z) ={ 1 \over {1-0.7z^-1}}$, how ...
2
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1answer
209 views
Autoregressive modeling (linear prediction) of electrical transmission lines?
I've read that the reflection coefficients in speech processing (as computed by the Levinson-Durbin algorithm for solving the Yule-Walker equations) "represent the fraction of energy reflected back" ...
0
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1answer
765 views
How to create an AR filter in Matlab
My goal is to replicate the procedure described on pages 15-16 (1461-1462) in this paper, prior to adaptive mixture ICA (AMICA): Overlearning in Marginal Distribution-Based ICA: Analysis and Solutions
...
1
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1answer
257 views
autoregressive moving average code implementation
I am new to DSP and i am trying to take a wav (human speech) file and apply ARMA filter and plot its PSD graph in python.
I see that there are a lot of AR implementations but almost none ARMA. I ...
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2answers
355 views
Levinson Method
i have just one question about Levinson, my question is: can we apply this method to determine the coefficients for FIR filter? if yes, please help me !
this is an example:
...
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0answers
59 views
derive AR model based on the autocorrelation of jakes model
I am trying to derive the channel model based on the autocorrelation of Jakes model.
In step 2, i am trying to get rid of $s(n+1)$ by inserting it to $s(n-k)$ in which the limit will change. However i ...
2
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1answer
319 views
Predicting account balance based on historical data
Given the values of a bank account balance over time (see figure below as an example), how can one predict the account balance at a given date in the future ?
Should I just fit one linear regression ...
2
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1answer
80 views
Two-Box-Model of a nonlinear amplifier
A nonlinearity with memory can be modelled by a two-box-model, which consists of a filter and a memoryless nonlinearity. I am referring to chapter 5.3.2 of the book "Simulation of Communication ...
1
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1answer
144 views
Fourier transform relationship
I am having trouble understanding the relationship between a frequency function and it's Inverse Fourier transform.
The Frequency function is
$$\frac{1+0.8(e^{-j 2\pi f}+e^{j 2\pi f})+0.64}{1+1.4\...
1
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1answer
210 views
Physically understanding autoregressive model (really basic question)
I would like to basically understand what an autoregressive model is used for (so I don't really attempt maths in the answers).
I just started a signal processing course and the model was introduced.
...
1
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2answers
598 views
Practical examples of ARMA model
I am studying the Kalman filter and its basic implementation, and it was asked to use the filter to estimate a signal observed in noise
$$y(n) = x(n) + v(n)$$
where $v(n) \sim \mathcal{N}(0, \sigma^2)$...
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1answer
590 views
How to estimate the autocorrelation from nonuniformly spaced data
Assume a continues-time random process $X(t)$ sampled nonuniformely in time to acquire discrete signal $x[n]$. The sampling times are known but the autocorrelation is not. Is there an accurate ...
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1answer
158 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)&...
0
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1answer
75 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 ...
0
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1answer
621 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 ...
1
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1answer
278 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
242 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 ...
2
votes
1answer
4k 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 ...
1
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0answers
138 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)?
0
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1answer
302 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 ...
2
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0answers
234 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 ...
0
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0answers
104 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
573 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
258 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 ...
2
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1answer
168 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 ...
1
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0answers
37 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 ...
2
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1answer
176 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
votes
1answer
229 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 ...
1
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0answers
226 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 ...
1
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1answer
575 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
3k views
How is `aicbic` or other matlab function used to find the AR order of specific data?
let us consider following matlab code
...
