> Thanks for your reply.
> For a 11 x 11 toeplitz autocorrelation matrix the eigen values i got
> are below.
> 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
indicate that there are two more components at frequencies close to
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
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
of sinusoidals present in the data set. So you need to know a lot
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
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
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
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
ago about efficient use of data when doung frequency estimation, check
and make sure you also read the correction I posted a few days