Hello Class, before you start doing Lab2, here are some background information you might want to read:
http://en.wikipedia.org/wiki/Window_function
http://en.wikipedia.org/wiki/Spectral_density
http://en.wikipedia.org/wiki/Orthogonal_transformation
Also as Additional Information: http://www.mathworks.com/help/matlab/ref/mtimes.html http://www.mathworks.com/help/matlab/ref/times.html
Q&A Section
Q: Anyone have an idea of how to compute the squared DFT magnitude in MATLAB? Is this the sum of pixels across the window multipled by cos(n)+isin(n) where n is the location between 0-64 in the window?
A: I would just x.^2 to be honest :)
Q: What does window function do?
A: Rememeber how rect goes to sinc from lab1? Everytime you sample an input segment and perform FFT, you are essentially applying rectangle window to the input samples. Therefore to reduce the effect of artifacts, people apply different type of windows before applying orthogonal transforms.
Q: In the second part, why are we adding 127 to each pixel value before displaying them, instead of scaling them to 0 - 255? Because, in my understanding, adding 127, would increase the (0,0) frequency component, and thus giving us the illusion that the image is smoother.
A1: I think it's just for visualization. For me, min(min(y)) = -121.79 and you can't display that. So, shifting by 127 makes pixel values non-negative.
