Questions tagged [autoregressive-model]
The autoregressive-model tag has no usage guidance.
80
questions
0
votes
0answers
25 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
0answers
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 ...
1
vote
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 $$v(n)=\sum_{k=0}^{m_{0}}b_ku(n-k)+\sum_{k=1}^{n_{0}}a_{k}...
1
vote
0answers
19 views
How to select the ARMA model parameters?
I have a series of data containing 120,000 points. The mean of each N(=60) point is zero. I want to forecast the next 60 points using the ARMA model. My question is, specificaly, how to choose the ...
1
vote
1answer
48 views
How to get velocity from PSD graph
Hello everyone!
I have a graph, which is Spectra inside cavity. PSD vs. frequency.
I need to get velocity [m/s] from PSD [dB/Hz].
Does anyone know how to do that?
2
votes
0answers
66 views
Ringing/Oscillation in the reconstructed Periodogram
I have an original periodogram that I need to model with autoregressive process. However the model isn't right as it is not fitted well to the original periodogram.
I am suspecting I am doing ...
0
votes
0answers
25 views
When is Markov a Martingale
I have two questions and I am very confused about the concepts
Can a Markov process of order one also be a a Martingale?
Is any Markov process of order one also a Martingale?
For 1. I would say yes, ...
0
votes
1answer
76 views
What are the most suitable methods for correcting sudden DC offsets or baseline offset? and Why? See the image for the use-case or example
The signal values should not get affected by the correction. Most methods I found were related to baseline drift or exponential baseline shift/decay. I am unable to find a method suitable for my use ...
2
votes
2answers
123 views
Extrapolation of sinusoidal signal
Let there be a discrete signal that is the sum of sinusoidals and can be described by
$$s(n)=\sum_i A_i \mathrm{sin}(2\pi f_i \frac{n}{f_s}+\phi_i)$$
where $A_i, f_i, \phi_i$ are unknown but fixed ...
0
votes
0answers
23 views
Compute objective speech quality from Anritsu data
I want to compute an objective speech quality however what I have right now is the Anritsu raw data (layer between the Base Station Controller and the Mobile Switching Center), this raw data does not ...
0
votes
1answer
60 views
ARMA Filter Output Stationary and set up?
I have questions regarding ARMA Filters.
Is the output of a ARMA Filter stationary or just wide sense stationary?
I do know that you can obtain an ARMA filter by connecting an MA filter with an AR ...
0
votes
1answer
80 views
Implementing the noisy AR(1) Process
I'm trying to implement noisy AR(1) process and plot it. The observed noisy sequence x(n) = s(n) + w(n) where variance of w(n) = 0.2.
s(n) is defined as an AR(1) process with s(n) = 0.5 s(n-1) + e(n)...
0
votes
1answer
121 views
estimation of ARMA(1,1) with MA parameter greater than 1
I am working with the following simple ARMA(1,1) model:
$$
z_{t+1} = \phi z_{t} + \theta\varepsilon_{t} + \varepsilon_{t+1}
$$
In my case $\theta$ depends on some other parameters, and, therefore, I ...
0
votes
1answer
89 views
Linear prediction and filter stability
I am currently trying to implement an iterative block-wise algorithm in which AR coefficients are computed for each block.
There is a issue with my code where values get too large, and I was ...
0
votes
0answers
411 views
How to find Coefficients of Autoregressive (AR) model using least means square (LMS) Algorithm without having future signal?
I want to do two things.
Estimating Coefficients of AR model using LMS
Using Coefficients found in step 1 and predict future samples of a signal using AR equation.
I don't have a desired signal so I ...
0
votes
0answers
44 views
What is prewhitening filter mode?
In this paper, the following prewhitening filter is described:
$$
C(z) = \sum_{k=0}^n c_{k}z^{-k}
$$
where $n$ and $c_k$ are known.
The paper also describes the values $C(\lambda_{k})$, with $\...
1
vote
1answer
192 views
Cost function for LTI system identification
I am currently reading and trying to understand a paper (Kulkarni and Colburn, 2004) that utilizes system identification methods to approximate head-related transfer functions.
The general approach ...
0
votes
1answer
152 views
How to characterize this whitening filter?
A little bit of background: I am interested in whitening in the least-square estimation.
In this sense, consider a univariate signal $y$. Assuming the covariance of $y$ is $\mathbf{A}\sigma^2$. ...
1
vote
0answers
348 views
Zero-padding vs. nonzero-padding in computation of auto-correlation with FFT
Isn't the usual zero-padding in the computation of the auto-correlation function with FFT just one of many possible extrapolations of the original signal?
If I have a measured signal which has good ...
4
votes
1answer
270 views
Fast Recursive 1D Signal Smoothing - IIR / Auto Regressive Implementation of Gaussian Smoothing
I have just begun to dive into the field of signal processing, but there is the need to program a digital filter, that has to smooth a realtime signal from a sensor device. As far as I know, in my ...
0
votes
1answer
191 views
AR Modeling: Why residual is white noise?
I was going through AR modeling.
The AR model of a covariance stationary process can be expressed as:
$$x[n]=\sum\limits_{i=1}^{p} \alpha_i x[n-i] + \epsilon[n]$$
where $p$ is the model order and $...
1
vote
0answers
2k views
Linear Predictive Coding example in MATLAB
I have some data that is highly correlated and I wanted to see if I could try and encode it using linear predictive coding (LPC). Here is how I've been understanding the process:
Encoding
Generate ...
1
vote
0answers
133 views
Understanding linear predictive coding in MATLAB
I want to test my understanding of linear prediction by running it on some test data in MATLAB. The way I understand it is if I have some data that is correlated, I can encode the signal with linear ...
1
vote
1answer
106 views
Explanation of Spectral Line Splitting when AR process is overmodeled
In the book Statistical Digital Signal Processing and Modeling by Monson Hayes, it is shown (in section 8.5.1) that when an AR(2) process described by the following difference equation
$$x(n) = 0.9x(n-...
2
votes
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 ...
0
votes
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 ...
2
votes
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 ...
2
votes
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 ...
2
votes
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 ...
3
votes
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 ...
0
votes
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, ...
0
votes
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#...
0
votes
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 ...
0
votes
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 ...
0
votes
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 ...
2
votes
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" ...
0
votes
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
...
1
vote
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 ...
-1
votes
2answers
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:
...
1
vote
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 ...
2
votes
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 ...
2
votes
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 ...
1
vote
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
$$\frac{1+0.8(e^{-j 2\pi f}+e^{j 2\pi f})+0.64}{1+1.4\...
1
vote
1answer
293 views
Physically understanding autoregressive model (really basic question)
I would like to basically understand what an autoregressive model is used for (so I don't really attempt maths in the answers).
I just started a signal processing course and the model was introduced.
...
1
vote
2answers
1k views
Practical examples of ARMA model
I am studying the Kalman filter and its basic implementation, and it was asked to use the filter to estimate a signal observed in noise
$$y(n) = x(n) + v(n)$$
where $v(n) \sim \mathcal{N}(0, \sigma^2)$...
0
votes
1answer
1k views
How to estimate the autocorrelation from nonuniformly spaced data
Assume a continues-time random process $X(t)$ sampled nonuniformely in time to acquire discrete signal $x[n]$. The sampling times are known but the autocorrelation is not. Is there an accurate ...
1
vote
1answer
668 views
How do I test stability of a MIMO system?
Let's say I have a system similar to two interconnected IIR filters described like this:
\begin{align}
x_1(t)&=a_{11} x_1(t-1)+a_{12} x_1(t-2) +a_{13} x_2(t-1) + a_{14} x_2(t-2)+y_1(t)\\
x_2(t)&...
0
votes
1answer
170 views
Different results for different orders of estimating AR model using Yule-Walker equations
I'm trying to use MATLAB to estimate the AR parameters to the following filter:
$$H(z) = \frac{1}{1-0.5z^{-1}+0.25z^{-2} -0.25z^{-4}}$$
As I can see, the process at the output of this filter depends ...
0
votes
1answer
918 views
Determining the autocorrelation sequence from an AR model
I have the following equation:
$$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 ...
1
vote
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 ...
