aliasing and orthogonality

I worked on computing cosine distances (dot products) between different frequencies as they would appear in a data set with uniform time spacing and uniform exposure time, as compared to a similar data set but with non-uniform time spacing and exposure times. In the uniform case, the different frequencies are exactly orthogonal (that is the magic of the Fourier transform) but there are also exact aliases among frequencies above the Nyquist limit. That is, for every frequency there are many aliases at very high frequencies. In the non-uniform case, all of these aliases disappear, but at the cost that no two frequencies are exactly orthogonal any more.

No comments:

Post a Comment