Fri 3 Oct 2008
I derived this inverse fourier transform a couple months ago but never posted. I wanted to explain what these two solved math problems were and how they are useful in great detail. But I guess I will just be short and sweet. If you want a further explanation you will have to do the work.
Basically these two transforms are useful in Ultra Wide Band (UWB) communications. UWB has a very high bandwidth because it signals extremal short Gaussian pulses at a very high data rate. The two transforms I present analyze UWB Gaussian pulses in both the frequency and time domains.
Due to the short time domain of UWB, it occupies a very large frequency spectrum.