.. (לתיקייה המכילה) | ||
Matlab Part - Zeroing the DC DFT-component | |
In subsection c you need to implement a notch filter for zeroing all the DFT-domain components that are deteriorated by the interference ("noise" of vertical lines). While the interference affects also the 0-index DFT-component (also called the DC component), you should not zero this specific component since it represents the mean graylevel of the entire image (if you zero it you'll get a restored image of "texture" over a black background -- which is not what we want). |
Matlab Part - Real-Valued Result and Numerical Errors | |
Please note that the restored image (after the inverse-DFT) should be a real-valued signal (as the symmetry in the DFT domain should be preserved also after the notch filtering). However, note that due the numerical computations in Matlab you may get results that may seem complex-valued, however, with imaginary parts of a very small size (for example, with magnitude of less than 10^-5). These kind of numerical inaccuracies are acceptable. Also be aware to AVOID implicit casting that may provide you a perfectly real-valued restored image (you may do this casting only for the purpose of eliminating numerical errors). |
Question #3 | |
You may find the following instructions helpful: 1. Express the smoothed signal in a convolution form, where a smoothing filter defines the interval of the smoothing. The convolution form where the signal is the reflected+shifted function may be easier to use in this question. 2. Use the convolution form of the smoothed signal to express its inner-product with the Fourier function. Develop the expression for the inner-product using the periodicity properties of the periodic-extension of the signal, and the periodicity of the Fourier function. 3. You should get an expression that includes the inner-product of the signal (not in its periodic extension form) with the Fourier function over the interval between 0 to 1. 4. Show that the inner product of the smoothed signal with the Fourier function satisfies the definition of N0-bandlimitedness. |