> Hi

> Thanks for your reply.

> For a 11 x 11 toeplitz autocorrelation matrix the eigen values i got

> are below.

> 0.4687

> 0.7427

> 0.7700

> 0.9202

> 0.9706

> 1.1414

> 1.2223

> 4.7889

> 4.7909

> 15.4860

> 16.6119

> Even from this, my perception is that there are just two eigen values

> corresponding to the signal sub-space.

You *could* be right. On the other hand, the two ~4.8 eigenvalues

*may*

indicate that there are two more components at frequencies close to

the

two first frequencies.

Quote:> From, the FPE criterion ( calculated for autocorrelation matrices upto

> order 11 x 11) i found that order =2 minimized the FPE criterion. But

> i dont know if i have to check for higher orders of the autocorreltion

> matrix. Won't the higher order autocorrelation matrices be in much

> error? Please clarify this to me.

That's where insight, experience and voodoo comes in to play. Choosing

the "correct" order of the autocovariance/autocorrelation matrix is

all but a black art. It takes trial and error over long time to

develop

a "gut feeling" for what orders work.

There are some "rules of thumb" you may use. One strict requirement is

that the order P of your autocovariance matrix is higher than the

number D

of sinusoidals present in the data set. So you need to know a lot

about

what measurements you will make, already at the design stages of

your processing system. The other is that the order shouldn't be too

high. The rule of thumb I used was P=3/2 D, when I had played around

with my data a bit. Now, I used pre-recorded data in an off-line

processing situation, and had quite some freedom of choise. You may

not have that freedom of choise, and that would restrict your options.

Quote:> When i computed the eigen values of a higher order autocorrelation

> matrix (23x23)i got 4 eigen values greater than 12 and the rest of the

> eigen values were less than 5. This would indicate that there are 4

> complex sinusoids.

Sure it does. I would go for the AIC or some other type of order

estimator.

I don't know FPE, so I don't know how it works or its properties.

Quote:> Should i consider the higher order result or that of the lower order

> one? Is my assumption of higher order autocorrelation matrices being

> more in error right, when the data sample is of length just 40?

Ouch! This is a delicate matter. How many 40-length snapshots/frames

of

data do you have? You would want to average at least 40 frames in your

autocovariance estimate. If you have only one frame, you should be

very

careful, it may very well introduce artifacts as the "extra" number of

signals you found in the 23X23 case. I gave an outline in a post not

long

ago about efficient use of data when doung frequency estimation, check

out

http://groups.google.com/groups?hl=no&lr=&ie=UTF-8&selm=f56893ae.0303...

and make sure you also read the correction I posted a few days

afterwards.

Rune