Paper deadlines!!!

Lucky for me (Bobby), the deadline for my conference paper that was this Friday has been pushed back a week until midnight May 15. So this gives me the opportunity to write a little update here for friends and family; but not so much an opportunity that I can discuss something other than research. So here I present some pictures from Paris.


Clearly, we are only interested in those regions where the lower and upper bounds of D1(t) and D2(t), respectively, overlap. All other regions can be discarded since they do not meet our minimum similarity threshold. Today I worked on finding the lower bound of D1(t) as a function of approximation order. I am excited to reveal the details, but I am sensitive to the fact that this not the forum to do so. After I am finished with this note, I will work on the upper bound for D2(t).

The eXtensible Fourier transform (XFT) takes an L2 function from the reals (or complex, actually) into a three-dimensional space of frequency, scale, and translation. Various planes in this space are equivalent to traditional analysis methods, such as Gabor analysis (e.g., short-term Fourier transform), and Wavelet analysis; and thus allow an inverse transformation back. My colleague Guillaume is interested in exploring this space to find information relevant for studying room impulse responses. I am interested in exploring the XFT from a more formal mathematical perspective with general signal processing in mind. In fact, greedy iterative descent pursuit approaches to sparse approximation can be seen as working in this XFT space. A sparse atomic decomposition consists of points in this space, which I lovingly refer to as a "constellation."

Much Love!
-Bob.