Tutorial 8 - Examples in Signal Decomposition

Assignment 1

Write a function monocomponents() which decomposes signal with the following algorithm:

1. Choose $\tau$ and form the Hankel matrix $H$
2. Compute the EVD of $H$
3. Choose the significant eigenpairs of $H$
4. For each significant eigenpair $(\lambda,u)$
   1. Form the rank one matrix $M=\lambda uu^T$
   2. Define a new signal $y$ consisting of the elements in the first row and the last column of $M$
   3. Form the Hankel matrix $H(y)$
   4. Compute the EVD of $H(y)$
   5. Choose the significant eigenpairs of $H(y)$
   6. If $H(y)$ has only two significant eigenpairs, declare $y$ a mono-component, else go to step 4.

Test the algorithm on the note A4.

Assignment 2

Decompose your favorite music part, or the first bar of Beethoven's Piano Sonata No. 8 Op. 13.