Jerry Avins skrev:
> Thomas Arildsen wrote:
>> 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).
> 
> Would http://www.polyx.com/demo_covf.htm help?
> 

Thanks, I think there might be some ideas to help me solve the problem 
as well. I actually already have one method, but I would like to check 
it against some other known method.

Thomas Arildsen

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Thomas Arildsen wrote:
> 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).

Would http://www.polyx.com/demo_covf.htm help?

Jerry
-- 
Engineering is the art of making what you want from things you can get.
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Andor skrev:
> Thomas Arildsen wrote:
>> I have an ARMA process with known parameters. Are there general
>> expressions for variance and possibly autocorrelation of the output for
>> such processes?
> 
> Yes. If x[n] is a WSS stochastic process, and h[n] the impulse
> response of your (stable) ARMA filter, and y[n] the output of the ARMA
> filter, ie.
> 
> y[n] = x[n] * h[n],
> 
> then the autocorrelation r_y[n] is
> 
> r_y[n] = r_x[n] * r_h[n],
> 
> where r_h[n] = h[n] * h[-n] is the autocorrelation of the impulse
> response. The mean m_y of the process y[n] is the mean m_x of x[n]
> multiplied by the DC response of the ARMA filter,
> 
> m_y = m_x sum_k h[k].
> 
> The variance is sigma_y^2 = r_y[0].
> 
> Regards,
> Andor
> 

I have the PSD expression for the filter; I think I will try to inverse 
transform from that to the autocorrelation in stead.

Thomas Arildsen

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HardySpicer skrev:
> On Oct 3, 8:43 pm, Thomas Arildsen <comp-dsp.es-
> aau...@spamgourmet.com> wrote:
 >
>> Would that be "Introduction to Stochastic Control Theory" from 1970?
>> What is meant by 'a set of tables'? Are they tables of calculated
>> variances and/or correlation values for specific ARMA configurations or
>> expressions for calculating these? I am looking for the latter.
>>
>> Thomas Arildsen
> 
> Yes! It's formula based on the ARMA coefficients for variance orders
> and yes it's variances.
> 
> Hardy
> 

Great, thank's. It seems to have been reprinted on Dover in 2006 and is 
available pretty cheap on Amazon. I'll give it a try.

Thomas Arildsen
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My real adress is at es dot aau dot dk for user tha.

Thomas Arildsen wrote:
> I have an ARMA process with known parameters. Are there general
> expressions for variance and possibly autocorrelation of the output for
> such processes?

Yes. If x[n] is a WSS stochastic process, and h[n] the impulse
response of your (stable) ARMA filter, and y[n] the output of the ARMA
filter, ie.

y[n] = x[n] * h[n],

then the autocorrelation r_y[n] is

r_y[n] = r_x[n] * r_h[n],

where r_h[n] = h[n] * h[-n] is the autocorrelation of the impulse
response. The mean m_y of the process y[n] is the mean m_x of x[n]
multiplied by the DC response of the ARMA filter,

m_y = m_x sum_k h[k].

The variance is sigma_y^2 = r_y[0].

Regards,
Andor

On Oct 3, 8:43 pm, Thomas Arildsen <comp-dsp.es-
aau...@spamgourmet.com> wrote:
> HardySpicer skrev:
>
>
>
> > On Oct 3, 1:02 am, Thomas Arildsen <comp-dsp.es-
> > aau...@spamgourmet.com> wrote:
> >> 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).
>
> >> Thomas Arildsen
>
> > There is a set of tables in a book by Karl Astrom - the old 1970s
> > book.
>
> > Hardy
>
> Would that be "Introduction to Stochastic Control Theory" from 1970?
> What is meant by 'a set of tables'? Are they tables of calculated
> variances and/or correlation values for specific ARMA configurations or
> expressions for calculating these? I am looking for the latter.
>
> Thomas Arildsen
>
> --
> All email to sender address is lost.
> My real adress is at es dot aau dot dk for user tha.

Yes! It's formula based on the ARMA coefficients for variance orders
and yes it's variances.

Hardy

HardySpicer skrev:
> On Oct 3, 1:02 am, Thomas Arildsen <comp-dsp.es-
> aau...@spamgourmet.com> wrote:
>> 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).
>>
>> Thomas Arildsen
> 
> There is a set of tables in a book by Karl Astrom - the old 1970s
> book.
> 
> Hardy
>

Would that be "Introduction to Stochastic Control Theory" from 1970?
What is meant by 'a set of tables'? Are they tables of calculated 
variances and/or correlation values for specific ARMA configurations or 
expressions for calculating these? I am looking for the latter.

Thomas Arildsen

-- 
All email to sender address is lost.
My real adress is at es dot aau dot dk for user tha.

On Oct 3, 1:02 am, Thomas Arildsen <comp-dsp.es-
aau...@spamgourmet.com> wrote:
> 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).
>
> Thomas Arildsen
> --
> All email to sender address is lost.
> My real adress is at es dot aau dot dk for user tha.

There is a set of tables in a book by Karl Astrom - the old 1970s
book.

Hardy

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).

Thomas Arildsen
-- 
All email to sender address is lost.
My real adress is at es dot aau dot dk for user tha.