Questions tagged [autoregressive-model]

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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: ...
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102 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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2answers
63 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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19 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 ...
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1answer
48 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?
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66 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 ...
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25 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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1answer
76 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 ...
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2answers
123 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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23 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 ...
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1answer
60 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 ...
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1answer
80 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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1answer
121 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 ...
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1answer
89 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 ...
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411 views

How to find Coefficients of Autoregressive (AR) model using least means square (LMS) Algorithm without having future signal?

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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44 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 $\...
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1answer
192 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 ...
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1answer
152 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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348 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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1answer
270 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 ...
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1answer
191 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 $...
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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 ...
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0answers
133 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 ...
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1answer
106 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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1answer
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 ...
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1answer
141 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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1answer
480 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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2answers
103 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 ...
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1answer
671 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
125 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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1answer
292 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
52 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
2k 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 ...
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1answer
163 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 ...
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1answer
652 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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1answer
267 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" ...
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1answer
1k 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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1answer
568 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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660 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
86 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 ...
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1answer
733 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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1answer
95 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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1answer
166 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\...
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1answer
293 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. ...
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2answers
1k 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
1k 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
668 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
170 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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1answer
918 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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1answer
362 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 ...