Questions tagged [autoregressive-model]

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Why use an ARMA process theory instead of just performing linear regression?

I am studying ARMA processes. At the end of the course the professor told us that estimating the next sample in an arma process using past of length $p$ (so performing a projection of $X_t$ on $\text{...
Robert Laplace's user avatar
2 votes
0 answers
28 views

Haykin - permissible region for asymptotic stationarity of 2 parameter AR process

My question is about an example in Adaptive Filter Theory, Haykin 4th ed (refer figures 1.8 and 1.10 of Haykin). We want to determine the region for asymptotic stationarity of an AR process in the 2D ...
dspcats's user avatar
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Reconstruction of original signal after minimum phase filter

The question is pretty self explanatory. I want to know if it is possible to recover a signal originally injected into noisy data (coloured gaussian noise) after whitening the data with an AR minimum ...
GWSurfer's user avatar
2 votes
2 answers
382 views

Why is ARMA preferred instead of AR?

ARMA basically is an AR model which considers past inputs to the filter as well. But what is the benefit of taking past inputs to the filter if we are considering real-time processes which are all ...
Kuchi Yashwanth's user avatar
1 vote
0 answers
27 views

How to show that the autocorrelation function of the given discrete function is this for autoregressive model(AR(2))?

This question is related to white noise representation of WSS sequences using AR(2) (autoregressive) model The function is given as: $$x(k)=\frac{1}{p_1-p_2}(p_1^{k+1}-p_2^{k+1})w[k]u[k]$$ where $w[k]$...
Userhanu's user avatar
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1 answer
106 views

Deterministic process, what is it ? how can i get a better intuition for it?

so I was following this code where the author cleans the data for a time series problem. He does some feature engineering , all is well and good until he does this ...
Taqi Hussain's user avatar
2 votes
1 answer
113 views

difference in the spectral densities of autoregressive sequence by FFT and analytical solution

I want to obtain the power spectral density (PSD) of an autoregressive sequence, AR(1). The analytical solution according to this reference (page 12) is For $X_t = \phi_1X_{t-1}+W_t, W_t \sim N(0,\...
Jayyu's user avatar
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4 votes
1 answer
160 views

Frequency representation of relaxation processes

I simulated a discrete sample of a variable whose autocorrelation function (ACF) should theoretically be composed of a sum of exponential-like functions. My goal is to represent it in the frequency ...
user1420303's user avatar
0 votes
1 answer
160 views

Given an AR signal, find its PSD, its autocorrelation function

I am studying discrete-random signal processing, Could anyone tell me by an example or reference what it means by the following? Given an AR signal, find its PSD (power spectral density), its ...
Marso's user avatar
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2 votes
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450 views

How to compute the theoretical power spectrum of a first order autoregression (AR1) model

I'm trying to figure out how to compute the theoretical power spectrum of a first-order autoregression model (AR1). The AR1 model is given as $x_i = r_1 x_{i-1} + e_i$ where: $x_i$ is real-valued ...
Jason's user avatar
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2 answers
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System identification for a single-input-single-output-system

Let $u(n)$ be the input and $v(n)$ the output of a single-input-single-output system described by the Auto-Regressive-Moving-Average equation $$v(n)=\sum_{k=0}^{m_{0}}b_ku(n-k)+\sum_{k=1}^{n_{0}}a_{k}...
SISO's user avatar
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1 vote
0 answers
30 views

How to select the ARMA model parameters?

I have a series of data containing 120,000 points. The mean of each N(=60) point is zero. I want to forecast the next 60 points using the ARMA model. My question is, specificaly, how to choose the ...
JES0's user avatar
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1 vote
1 answer
158 views

How to get velocity from PSD graph

Hello everyone! I have a graph, which is Spectra inside cavity. PSD vs. frequency. I need to get velocity [m/s] from PSD [dB/Hz]. Does anyone know how to do that?
look_at_formula's user avatar
2 votes
0 answers
80 views

Ringing/Oscillation in the reconstructed Periodogram

I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram. I am suspecting I am doing ...
Sam Gomari 's user avatar
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0 answers
48 views

When is Markov a Martingale

I have two questions and I am very confused about the concepts Can a Markov process of order one also be a a Martingale? Is any Markov process of order one also a Martingale? For 1. I would say yes, ...
gkc's user avatar
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1 answer
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What are the most suitable methods for correcting sudden DC offsets or baseline offset? and Why? See the image for the use-case or example

The signal values should not get affected by the correction. Most methods I found were related to baseline drift or exponential baseline shift/decay. I am unable to find a method suitable for my use ...
user55240's user avatar
2 votes
2 answers
376 views

Extrapolation of sinusoidal signal

Let there be a discrete signal that is the sum of sinusoidals and can be described by $$s(n)=\sum_i A_i \mathrm{sin}(2\pi f_i \frac{n}{f_s}+\phi_i)$$ where $A_i, f_i, \phi_i$ are unknown but fixed ...
SignalExtrapChicago's user avatar
0 votes
0 answers
28 views

Compute objective speech quality from Anritsu data

I want to compute an objective speech quality however what I have right now is the Anritsu raw data (layer between the Base Station Controller and the Mobile Switching Center), this raw data does not ...
Nassereddine Belghith's user avatar
0 votes
1 answer
85 views

ARMA Filter Output Stationary and set up?

I have questions regarding ARMA Filters. Is the output of a ARMA Filter stationary or just wide sense stationary? I do know that you can obtain an ARMA filter by connecting an MA filter with an AR ...
Noobcoder's user avatar
0 votes
1 answer
293 views

Implementing the noisy AR(1) Process

I'm trying to implement noisy AR(1) process and plot it. The observed noisy sequence x(n) = s(n) + w(n) where variance of w(n) = 0.2. s(n) is defined as an AR(1) process with s(n) = 0.5 s(n-1) + e(n)...
Jason's user avatar
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1 vote
1 answer
227 views

estimation of ARMA(1,1) with MA parameter greater than 1

I am working with the following simple ARMA(1,1) model: $$ z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1} $$ In my case $\theta$ depends on some other parameters, and, therefore, I ...
ABK's user avatar
  • 171
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1 answer
114 views

Linear prediction and filter stability

I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block. There is a issue with my code where values get too large, and I was ...
Jonas Schwarz's user avatar
4 votes
1 answer
844 views

Learning the Coefficients of Auto Regressive (AR) Model Using Least Mean Squares (LMS) Filter for Signal Prediction

I want to do two things. Estimating Coefficients of AR model using LMS Using Coefficients found in step 1 and predict future samples of a signal using AR equation. I don't have a desired signal so I ...
Abeeha's user avatar
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0 answers
56 views

What is prewhitening filter mode?

In this paper, the following prewhitening filter is described: $$ C(z) = \sum_{k=0}^n c_{k}z^{-k} $$ where $n$ and $c_k$ are known. The paper also describes the values $C(\lambda_{k})$, with $\...
Cristian M's user avatar
1 vote
1 answer
281 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 ...
Jonas Schwarz's user avatar
0 votes
1 answer
240 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 $\mathbf{A}\sigma^2$. ...
hhn's user avatar
  • 3
1 vote
0 answers
561 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 ...
oliver's user avatar
  • 266
4 votes
1 answer
446 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 ...
Lemonbonbon's user avatar
0 votes
1 answer
348 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 $...
user7080's user avatar
1 vote
0 answers
3k 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 ...
compscinoob's user avatar
1 vote
0 answers
209 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 ...
compscinoob's user avatar
1 vote
1 answer
158 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-...
MaxFrost's user avatar
  • 359
2 votes
1 answer
2k 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 ...
MaxFrost's user avatar
  • 359
0 votes
1 answer
199 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 ...
blue_note's user avatar
  • 123
2 votes
1 answer
1k 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 ...
Aditya TB's user avatar
  • 129
2 votes
2 answers
177 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 ...
MisterFilter's user avatar
3 votes
1 answer
942 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 ...
Abhinav's user avatar
  • 133
4 votes
2 answers
152 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 ...
Abeeha's user avatar
  • 87
0 votes
1 answer
606 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, ...
XRaycat's user avatar
  • 147
0 votes
2 answers
58 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#...
SKM's user avatar
  • 601
0 votes
1 answer
3k 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 ...
SKM's user avatar
  • 601
0 votes
1 answer
174 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 ...
user394872's user avatar
0 votes
1 answer
805 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 ...
Ragnar's user avatar
  • 7
2 votes
1 answer
285 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" ...
Andrew D'Addesio's user avatar
0 votes
1 answer
2k 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 ...
user avatar
2 votes
1 answer
616 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 ...
Richard's user avatar
  • 31
-1 votes
2 answers
764 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: ...
Midou's user avatar
  • 1
1 vote
0 answers
113 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 ...
Ray's user avatar
  • 11
4 votes
2 answers
803 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 ...
eLearner's user avatar
  • 149
2 votes
1 answer
115 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 ...
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