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I am currently taking an graduate-level Advanced Signal Processing class and I have a midterm soon. However, the midterm is not only open-book but it is also open-internet and untimed. Now I have no previous exams of the professor but I do have one exam of a lower level signal processing course where the professor basically asked the derivation of the DCT from the DFT having not even touched the DCT in that course. This is obviously a doable task but I mentioned this because it shows the type of questions the professor likes to ask. Stuff that cannot be easily found in textbooks and the like but stuff that is rather important. Keeping that in mind what are some important concepts related to the following topics that cannot be easily accessed in papers and textbooks?

  • Least Squares and Approximation Theory
  • Random Processes and System Modeling (AR, MA, ARMA)
  • Generalized Sampling Theorem with Linear Algebra Framework
  • DFT, DCT, Hartley Transform, Hilbert Transform, Hadamard Transform and KL Transform

A lot of the things that the professor does in class, I struggle to find in textbooks. For example, while looking for a proper derivation of the DCT I went through many papers and textbooks (including of the original inventor) before I found it in Proakis and Manolakis, DSP 2006 2nd Edition section 7.5.1. So essentially I am looking for concepts and resources that are quite relevant but might be a bit advanced for the surface level introduction to these topics. Another example that I have is how the Fourier Transform decorrelates WSS Processes which came up during our discussion of the KL Transform, and he was forced to admit this after one of the students made the connection. Now most of the readily available literature and resources on KL Transforms goes into the Image Processing aspect and usage of it but rarely can I find such a gem of a conclusion related to KL Transforms.

Anything related to these topics in terms of critical concepts and/or resources would be appreciated!

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    $\begingroup$ Plot twist: Sherlock is the professor. 🤣 $\endgroup$
    – Peter K.
    Commented Mar 27 at 16:04
  • $\begingroup$ @PeterK. shhh xD. On a serious note I would appreciate any guidance in this matter $\endgroup$ Commented Mar 27 at 16:36

1 Answer 1

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  1. How would you compress image using the KLT concept?
    Should be done by building a matrix of patches and applying PCA.
  2. The equivalence of the weighted least squares and Mahalanobis based distance.
    Show that the weighted least squares could be formulated as a regular least squares using the distance based on Mahalanobis distance.
  3. Show equivalence of the Wiener Filter and the least squares solution with a prior.
  4. Build the DCT transform using DFT blocks.
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