## Question about the z-transform for ARMA modelling

Started by in comp.dsp16 years ago 5 replies

Hello! I have some questions about the z-transform and what to use it for in for example ARMA-filters. I know it is used to find poles and...

Hello! I have some questions about the z-transform and what to use it for in for example ARMA-filters. I know it is used to find poles and zeros, but what else? Consider an ARMA filter: y(t)+a1*y(t-1)+a2*y(t-2)=x(t)+c1*x(t-1)+c2*x(t-2) After z-tranformation it can be written: Y(z)=H(z)*X(z) where ...

## Finding ARMA coefficients

Started by in comp.dsp13 years ago 3 replies

Hello! I have a problem to understand ARMA filter dsign. I would be thankful to tell me in detail how can find coefficients of the ARMA filter...

Hello! I have a problem to understand ARMA filter dsign. I would be thankful to tell me in detail how can find coefficients of the ARMA filter for any time-series data. Thank you.

## ESTIMATING MA COEFFICIENT FROM ARMA

Started by in comp.dsp11 years ago 12 replies

Hi All, I am working on ARMA coefficient determination using a data sequence. I have no idea of the underlying system from which the data was...

Hi All, I am working on ARMA coefficient determination using a data sequence. I have no idea of the underlying system from which the data was generated . What i only have is the data and thsi si as shown in the vector form below. If the data is labeled d = [d(1),d(2),d(3),d(4),d(5),d(6),d(7),d(8),d(9),d(10),d(11),...... d(45)] if the ARMA equation is y(n) = a(1)y(n-1) + a(2)y(n-2) + b...

## Approximate ARMA process by AR process

Started by in comp.dsp11 years ago 8 replies

Is there an optimal, or perhaps just 'standard', method of approximating some given ARMA process (the coefficients and order are given and I...

Is there an optimal, or perhaps just 'standard', method of approximating some given ARMA process (the coefficients and order are given and I assume zero-mean unit-variance white Gaussian input) by an AR process? I thought about generating an output sequence from the ARMA process and then estimating AR parameters from that data, but I would like to be able to determine them directly from t...

## how use ARMA coefficients

Started by in comp.dsp10 years ago 3 replies

Hi guys, for the first time i'm looking information about arma models. it isn't my aim learn how to built it but just use the coefficients i...

Hi guys, for the first time i'm looking information about arma models. it isn't my aim learn how to built it but just use the coefficients i already have. the coefficients are obtained with a NLS algorithm so, i've a time serie in a spreadsheet and coefficients for AR(2) and MA(2). what formula have i to use to fit the serie for MA(2), AR(2), and ARMA(2,2)? tnx!

## from state space to arma

Started by in comp.dsp12 years ago 6 replies

Hi all, I would be greatfull if someone could advice me on the following problem. I have a state space model with matrices A,B,C...

Hi all, I would be greatfull if someone could advice me on the following problem. I have a state space model with matrices A,B,C (x(k+1)=Ax(k)+Bu(k),state eq. y(k)=Cx(k)) how can from this state space form to pass in a form of arma.Can i use rls to estimate arma coefs?

## Hilbert transform of ARMA filter

Started by in comp.dsp15 years ago 6 replies

Suppose I have an ARMA filter of order N with known A and B coefficients. Does there exist another ARMA filter of order N whose impulse...

Suppose I have an ARMA filter of order N with known A and B coefficients. Does there exist another ARMA filter of order N whose impulse response (and output) is the Hilbert transform of the original filter? If so, what is the expression relating the two sets of coefficients? Thanks! This message was sent using the Comp.DSP web interface on www.DSPRelated.com

## ARMA modeling

Started by in comp.dsp12 years ago 10 replies

I am looking for an algorithm to model a system using an ARMA filter. The input and the desired output are available. Is there an iterative...

I am looking for an algorithm to model a system using an ARMA filter. The input and the desired output are available. Is there an iterative algorithm that can give a global optimum solution ? Any good reference ? Regards Tom

## From Z-transform to Laplace

Started by in comp.dsp10 years ago 3 replies

Hello, I have a transfer function from ARMA or AR model having some high order. I want to obtain H(s). My approach is to assume that H(s) will...

Hello, I have a transfer function from ARMA or AR model having some high order. I want to obtain H(s). My approach is to assume that H(s) will have a form that will result in a high H(z) ARMA/AR model , and find a relation between these two!! I would appertiate any suggestion or comment,

## Which approach is better to estimate the ARMA model parameters

Started by in comp.dsp4 years ago 2 replies

I have a task to estimate an ARMA system model parameters. The nominator and denominator orders are known. The ARMA parameters could be...

I have a task to estimate an ARMA system model parameters. The nominator and denominator orders are known. The ARMA parameters could be estimated from the time domain or frequency domain through minimizing the mean-squared error of the measured and the system modeled signals. Which domain is preferred to estimate the system model? Note for the frequency domain, the magnitude of the frequency erro...

## ARMA model statistical properties

Started by in comp.dsp12 years ago 8 replies

I have an ARMA process with known parameters. Are there general expressions for variance and possibly autocorrelation of the output for such...

I have an ARMA process with known parameters. Are there general expressions for variance and possibly autocorrelation of the output for such processes? I can find the above for an order-(1,1) process in for example Shanmugan & Breipohl's "Random Signals" (Wiley, 1988), but is it possible for higher orders? If it helps, I would be happy to confine the processess in question to order (p,p...

## ARMA parameter estimation from noisy observations

Started by in comp.dsp11 years ago 7 replies

Hi I am trying to fit an (8,5) ARMA model to a time series in the presence of additive white noise. The SNR is around 10-20dB. So far I have...

Hi I am trying to fit an (8,5) ARMA model to a time series in the presence of additive white noise. The SNR is around 10-20dB. So far I have tried the armax function from the Matlab system identification toolbox, the ARMASA toolbox for Matlab and a reduced statistics algorithm. Unfortunately I have found that these methods are unreliable when the SNR is less than about 60dB, and the models p...

## Re: System Identification

Started by in comp.dsp11 years ago 1 reply

On Jul 1, 6:02=A0am, Rune Allnor wrote: > Therrien suggestes that the term 'Prony method' applies to > ARMA estimation where the A() and...

On Jul 1, 6:02=A0am, Rune Allnor wrote: > Therrien suggestes that the term 'Prony method' applies to > ARMA estimation where the A() and B() coefficents are > estimated in separable steps. At the risk of embarrassing myself, since it's been literally 25 years since I worked with this stuff, I recall Prony's Method to model the impulse response of an ARMA system as t

## estimating data using parametric methods

Started by in comp.dsp11 years ago 4 replies

Hi! I have some questions which i would have some answers to. I have some data that i have to study using its spectra. To get the spectra i use...

Hi! I have some questions which i would have some answers to. I have some data that i have to study using its spectra. To get the spectra i use AR and ARMA estimators. How do i choose an AR and ARMA method. I have used Least-square method and two stage least-square method because i have heard that yule walker can for nearly periodic signals estimate incorrect parameters. But i have also heard ...

## multivariate cepstrum

Started by in comp.dsp15 years ago 2 replies

Hi I know what the cepstrum of a univariate ARMA model is. Does anyone know how to extend the idea to multivariate ARMA processes?...

Hi I know what the cepstrum of a univariate ARMA model is. Does anyone know how to extend the idea to multivariate ARMA processes? Recomendations for a good textbook? MODEL: x(t) = SUM( k=1..P, a(k)x(t-k) ) + SUM( k=1..Q, b(k)w(t-k) ) where w(t) ~ N(0,S) are normally distributed multivariate random variables, and x(t) is a z by 1 vector. DEFINITION FOR UNIVARIATE CASE, z=1: Si...

## What is wrong with my ARMA implementation (IIR)?

Started by in comp.dsp5 years ago 7 replies

Hi, I simulate an ARMA (3,3) in...

Hi, I simulate an ARMA (3,3) in Matlab/Simulink: a_t-0.9391a_(t-1)+2.8763a_(t-2)-2.9372a_(t-3)=0.0376e_t+0.1127e_(t-1) +0.1127e_(t-2)+0.0376e_(t-3) First, it is transformed: a_t=0.9391a_(t-1)-2.8763a_(t-2)+2.9372a_(t-3)+0.0376e_t+0.1127e_(t-1) +0.1127e_(t-2)+0.0376e_(t-3) According to the source paper, e_t~N(0, 0.01^2), I find that the output a_t has extremely huge magnitude signal a...

## Partial Fraction Decomposition in c++

Started by in comp.dsp13 years ago 6 replies

Hello! In order to calculate the Amplitude of a pole of an ARMA filter, I realise that I have to do a partial fraction decomposition (PFD) of...

Hello! In order to calculate the Amplitude of a pole of an ARMA filter, I realise that I have to do a partial fraction decomposition (PFD) of the ARMA filter transfer function. The PFD has to be done, so that I can calculate the residuum of the transfer function at each pole. I have the transfer function and have calculated the roots of the numerator and denominator polynomials, but have ...

## ARMA models

Started by in comp.dsp7 years ago 4 replies

Suppose you have a system B/A and you estimate using an AR method g/A2 where g is a constant, the rest ie B,A,A2 are polynomials in z^-1. Here I...

Suppose you have a system B/A and you estimate using an AR method g/A2 where g is a constant, the rest ie B,A,A2 are polynomials in z^-1. Here I am assuming that you cannot get A directly using an AR method since it is estimating an approximation of the zeros in the poles.So instead we call it A2. Then you estimate B/A = C using a MA method.(where C is another polynomial). Can

## what justify an AR model?

Started by in comp.dsp12 years ago 3 replies

If a time series is supposed to be generated by an AR model, how to justify such a supposition, what's the physical mechanism behind it? that...

If a time series is supposed to be generated by an AR model, how to justify such a supposition, what's the physical mechanism behind it? that is, why not model it by a MA or ARMA model? Is Yule-Walker the common and PRACTICAL way to find out the parameters of the AR model? Pls give some light on this.

## Estimate Observation Noise Variance

Started by in comp.dsp11 years ago 2 replies

Can anyone give some pointers on estimating observation noise variance from an observed set. I have an process (ARMA) that I am estimating the...

Can anyone give some pointers on estimating observation noise variance from an observed set. I have an process (ARMA) that I am estimating the parameters of (blind estimation, I don't know the input sequence, I only see the output), it would be useful to be able to have an estimate of the variance of the added white Gaussian observation noise. My understanding was that the following woul...