Jared McBride

Jared McBride

I am a PhD candatite in the University of Arizona Aplied Math GIDP

Meeting with Dr. Lin

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Today we meet came up with the following tasks for me to do:

  • Write a note on spectral factorization using the Kalman filter. This will be nice to have down in a clear, concise yet comprehensive way using consistent notation. I will include a description of the Kalman filter and where possible include intuition that may be useful.
  • Address this question: What information is missed after a single stage of whitening? We will have to explain why iterative whitening works. Additionally, I would like to repeat the experiment from here. That is, run 1000 realizations of a Gaussian process (or a harder process) and use this method to get a variance for the estimate of the power spectrum.
    • Can I make an example that requires more whitening, say, an arbitrary number of stages.
  • Write up a basic Kalman filter implementation and make sure it gets the same result as CKMS.
  • Clean up areas in code in which inverses are taken.

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Numerical Spectral Factorization by Kalman Recursion

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Here is note on spectral factorization using the Kalman recursions. It is mainly a restatement on the same material by Kailath. However there are a number of details that are made more transparent.

Question for Dr. Lin

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I am perhaps trying to be too technical. By I am curious, even if this doesn’t belong in the note that I am writing about spectral factorization. In the context of a state-space model,

Meeting with Dr. Lin

1 minute read

Published:

Had a brief meeting and reiterated points from last time.