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### AR(1) model (autoregressive process)

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```Hi

I have been trying to use the 'filter' function in matlab to produce a AR(1) signal. If I generate the input white noise array (x), how do I obtain positive coefficients to produce to output signal, AR(1)?

I understand that the 'aryule' function amoung others can give you the coefficients, but you need the AR(1) signal to start off with.

So my question is, if you are trying to produce an AR(1) signal, under what definitions do you create the coefficients?

```
 0
Reply Suvania 5/21/2010 1:43:05 PM

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```On 21 Mai, 15:43, "Suvania " <smoodl...@gmail.com> wrote:
> Hi
>
> I have been trying to use the 'filter' function in matlab to produce a AR(1) signal. If I generate the input white noise array (x), how do I obtain positive coefficients to produce to output signal, AR(1)?
>
> I understand that the 'aryule' function amoung others can give you the coefficients, but you need the AR(1) signal to start off with.
>
> So my question is, if you are trying to produce an AR(1) signal, under what definitions do you create the coefficients?

Your description of the task does not make sense, indication
that you need to read up on the basics. There are a number of
aspects you will need to sort out. The quick'n dirty key words:

- What characteristics of the signal the AR(p)
coefficient(s) signify
- How to select an AR(p) model
- How to select the coefficients of an AR(p) model
- How to generate the AR(p) signal
- How to represent AR(p) signal
- How to determine the order of the AR(p) model,
given the signal
- How to extract the coefficients of the AR(p)
model from the signal, given the order.

Rune
```
 0
Reply Rune 5/21/2010 2:09:54 PM

```"Suvania " <smoodliar@gmail.com> wrote in message <ht62l9\$t7e\$1@fred.mathworks.com>...
> Hi
>
> I have been trying to use the 'filter' function in matlab to produce a AR(1) signal. If I generate the input white noise array (x), how do I obtain positive coefficients to produce to output signal, AR(1)?
>
> I understand that the 'aryule' function amoung others can give you the coefficients, but you need the AR(1) signal to start off with.
>
> So my question is, if you are trying to produce an AR(1) signal, under what definitions do you create the coefficients?
>
>

Perhaps I should explain my task in more detail.

I have modeled a queuing system, and wish input various types of traffic and analyze the queuing behaviour. At the moment I am busy trying to model video traffic to input into my queue.

The specifications of video traffic that I am trying to replicate from a journal paper is as follows:

1) First order autoregressive model is used
2) frame length = 2ms
3) The mean of the video traffic is 72.7kb/s  (145.4 bits/frame length)
4) The standard deviation of the video traffic is 6.95kb/s (13.9 bits/frame length)

Since it was stated that an AR(1) model was being used, I analyzed,
y(n) = a1*y(n-1) + e(n)

I have researched that:
1) The AR(1) model to used to predict random processes
2) Only past values of the model OUTPUT, and present value of the model INPUT are used
3) 'a' is known as the model autoregression coefficients. They are used as weights in trying to use the past output values to predict the current output value. They are used to minimize the mean square value of the prediction error
4) The error term 'e(n)' is white Gaussian noise, with the mean of 0 and variance sigma^2.

The way that I have related this to video traffic is that the AR(1) signal represents the number of bits per frame length. The frame length number will be denoted as 'n' and the white Gaussian noise will be the input signal.

I am trying to produce an OUTPUT signal (bits/frame length = bits/2ms), based on an unknown INPUT and unknown coefficients. From what I understand, I should be getting on average 145.4 bits/frame length (OUTPUT SIGNAL). The length of deviation from this mean is 13.9 bits/frame length

The problems I am struggling to understand is as follows:

1) My specifications define the mean and standard deviation of the OUTPUT signal (bits/frame length). I am only generating my INPUT signal (white gaussian noise), with mean = 0, and variance = sigma^2. How do I inco-operate my specifications into my model?

2) Weighting Coefficient:
-> Since I am dealing with bits/frame I know I can't have a 'negative' amount of bits per 'n' state.
-> How to select AR(1) coefficients?

I have tried to understand AR models, and I am aware AR(1) is the simplest. Perhaps I am over thinking things, and lack a basic understanding. Please can you direct me, any help will be appreciated.
```
 0
Reply Suvania 5/22/2010 9:20:08 AM

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