Solution 10 Computational Intelligence Lab 2016
Note: The solution can now be found on the CIL website of FS16: Master solution (VPN required)
See Solution 7 from FS15.
- Formula (linear transformation or change of basis) applied to original signal x, given U:
- Inverse formula to obtain reconstructed signal applied to : (due to orthogonality of U)
- In both cases, we reconstruct the signal using only the frequencies of high magnitude, discarding the other components. So the rectangle spans over the whole frequency range, from a threshold value up to plus infinity. Here, we keep the lower frequencies (the ones on the left of the spectrum), so we get a low-pass filter. This de-noises the signal.
- False, because the signal on the top row is a continuous, sine-like signal, which is better suited for a Fourier Basis (global support).
- True, because the signal on the bottom row is localized.
- The peaks correspond to the most dominant frequencies of the original signal.