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Concept confused: covariance matrix of sine wav

Started by Yan.L July 28, 2003
Hi, experts,

What is covariance matrix of x[k]=sin(pi*k*f0)? (it contains no randomness).
Should it be dependent on k? nonstationary?

Then what is the optimal (Wiener) solution of this predictor?
x'[k]=w1*x[k-1]+w2*x[k-2];
d[k]=x[k];
e[k]=d[k]-x'[k];

w should satisfy Rx*w=p where Rx is the covariance matrix and seems to be singular.

If Rx is dependent on k, how to solve this?

Many thanks!
waters@starhub.net.sg (Yan.L) wrote in message news:<df850db4.0307272003.31e88b77@posting.google.com>...
> Hi, experts, > > What is covariance matrix of x[k]=sin(pi*k*f0)? (it contains no randomness). > Should it be dependent on k? nonstationary? > > Then what is the optimal (Wiener) solution of this predictor? > x'[k]=w1*x[k-1]+w2*x[k-2]; > d[k]=x[k]; > e[k]=d[k]-x'[k]; > > w should satisfy Rx*w=p where Rx is the covariance matrix and seems to be singular. > > If Rx is dependent on k, how to solve this? > > Many thanks!
This isn't homework, is it? Anyway, the first point you need to check out, is covariance functions/ matrixes of stationary processes. Next, you may (OK, will) find it useful to investigate what "the covariance coefficient of lag m" is all about. As for deterministic expressions as opposed to random data, check out the difference between "true covariance" and "estimated covariance". Once these concepts are in place, the answer on how to solve for w should be within easy reach. Rune