Questions tagged [autoregressive-model]

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54 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 ...
0 votes
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25 views

Particle Filter estimation: sinusoidal signal

I am designing a particle filter for the extraction of a sinusoidal wave with known frequency and sampling frequency from Gaussian noised biased measurements ($y=x+\text{bias}+\text{Noise}$) My state ...
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How to determine the area for the coefficients of an AR model to be asymptotically stable?

I am pretty new to this topic, and I am a little confused about the definition of asymptotically stable. If I have an AR model as follows $$y(t)=a_1y(t-1)+a_2y(t-2)+e(t)$$ How to define the area in ...
2 votes
1 answer
100 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,\...
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Predicting at différents steps

Let an autoregressive filter, with time step $T$ seconds, model a pink noise. Raw data is available at $f >> 1/T$. The model is trained on data undersampled and locally averaged (using a sliding ...
4 votes
1 answer
150 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 ...
0 votes
1 answer
56 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 ...
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35 views

2D space and 1D time evolution of a random field

I also asked this on math stack-exchange, but it is also relevant for the signal processing community. I want to develop a 2D random field and its change with time with constant velocity. My process: ...
2 votes
0 answers
250 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 ...
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1 vote
2 answers
70 views

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}...
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1 vote
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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 ...
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1 vote
1 answer
85 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?
2 votes
0 answers
73 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 ...
0 votes
0 answers
37 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, ...
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1 answer
137 views

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 ...
2 votes
2 answers
187 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 ...
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24 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 ...
0 votes
1 answer
75 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 ...
0 votes
1 answer
125 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)...
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1 vote
1 answer
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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 ...
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1 answer
100 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 ...
5 votes
1 answer
620 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 ...
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0 answers
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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 $\...
1 vote
1 answer
225 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 votes
1 answer
179 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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1 vote
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457 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 ...
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5 votes
1 answer
323 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 votes
1 answer
251 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 vote
0 answers
2k 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 vote
0 answers
169 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 vote
1 answer
134 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-...
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2 votes
1 answer
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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 ...
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1 answer
167 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 ...
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2 votes
1 answer
639 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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2 votes
2 answers
118 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 ...
3 votes
1 answer
768 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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4 votes
2 answers
137 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 ...
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0 votes
1 answer
364 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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2 answers
55 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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1 answer
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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 ...
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1 answer
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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 votes
1 answer
695 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 ...
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2 votes
1 answer
276 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 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 ...
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2 votes
1 answer
601 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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-1 votes
2 answers
702 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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1 vote
0 answers
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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 ...
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4 votes
2 answers
779 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 ...
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2 votes
1 answer
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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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1 vote
1 answer
168 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\...