42 karma · joined December 20, 2021
See also CUDA. Sure you can write a C to CUDA converter auto-vectorizer but its likely to have all sorts of bugs and usually never work right except in rare hand-tune cases. May as well just write CUDA from scratch if it is to be performant. Same for array processing, wanna array process? Use compiler for array processing like Fortran or ISPC.
The conception of the theorem is that if the signal being sampled is sufficiently integrable AND bandlimited AND the signal is uniformly sampled at at least the Nyquist rate over all time/space THEN then reconstruction of the bandlimited signal is exactly possible using the sinc interpolator. The proof is covered in "Shannon's original proof" in the Wikipedia article and most books on signal analysis such as Gaskill's Linear System book. Most EE people will have to do the proof as an intro course assignment in the first month of a DSP class.
OTOH, if you are not able to sample the function over all space or time AND the function happens to be periodic outside the interval you did sample THEN reconstruction of the bandlimited periodic signal is possible using the Dirchlet kernel.
If you are not able to sample the function overall space (from the first) AND that function is not periodic, you have small problems which occasionally become big problems if you are no careful. Most DSP books have a chapter about windowing discrete data and dealing with this conundrum. Basically, exact reconstruction is not guaranteed and context-specific techniques need to be employed to ensure desirable fidelity.
The reason we have multiple lenses sticking out of a phone is to achieve similar high image pixel counts at high sensitivity/low noise across wildly different fields of view (say 108 deg, 69 deg, 28 deg) and wildly different per-pixel angular fields of view in a cost effective manner. A single imaging block capable of seeing a whole 108 deg field of view wide camera image with the per-pixel angular field of view of the 28 deg telephoto imager is generally infeasible in a cost effective way unless you are IMAX.
More power to the folks who can stomach classical organ music though. You guys pay the bills for the rest of us who want to hear melodies we recognized.
However, the organ (particular symphonic organ and theatre variants) are frankly pretty adept at translations of music that is rhythmically and familiar to popular music trends of the last 60 years. In this case, the listener doesn't have to be nearly as intimately familiar with the trends of music between the 1700s and before the date their grandparents were born.
The lower the cost of living, the lower the cost of auditorium space. The lower the cost of auditorium space, the easier it is to get access to organs (to a point).
Misc tracks: https://www.youtube.com/watch?v=tzpQHz2dGX8 https://www.youtube.com/watch?v=3VN5DGw3OvA https://www.youtube.com/watch?v=Zm_vvBuH2ts
Also, even some of the classical works from folks like Ravel, Liszt and particularly have some ball busters if played on a big machine:
https://www.youtube.com/watch?v=pdrwazpZvAQ https://www.youtube.com/watch?v=VC3cZ-7-IoI .
TLDR: the folks that want to hear organs sound good go find other people that want to hear organs sound good and we have conventions and listen to organs sounding good.