3 ms·
After learning of the Fourier transform in school, I immediately became interested in this for obvious reasons, but never successfully wrapped my mind around it
by meltyness 4y ago
After learning of the Fourier transform in school, I immediately became interested in this for obvious reasons, but never successfully wrapped my mind around its employment usefully, beyond the jargon "wave localization."
The physical significance really arises from a place called the Huygens principle in mechanics, which supports claims about spatial wavefront propagation to state that at each timestep and point on the wavefront, another similar wave propagates, these subwaves are called wavelets.
- this-pony 4y agoI'm a doctoral student working in the direction of PDE's and function spaces. I have some colleagues that are using wavelets for numerics. They typically prove that certain wavelet bases are better suited for numerical approximation of certain types of problems. You can for instance think about if you have a signal mainly composed of square waves. Then it would be rather inefficient to decompose this signal in sines and cosines. For certain types of PDE's under certain type of geometrical restrictions, sometimes you can find a much better wavelet bases than just sines and cosines. My research is rather theoretical (so I don't do any numerics), so wavelets don't play a role for me.
- meltyness 4y agoI did my undergrad 10 years ago, and am essentially a hobbyist, myself currently working through Strang DE since I found Boyce uninstructive. The brief dialog on centered difference certainly raised my eyebrow, since Strang in an effort to more explicitly relate difference and differentials calls those out early, whereas the first time through the material I hadn't seen that interpretation until taking signals.