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I think the surprising commonality is conditional. So you won't see it unless you are focusing on physics or signal processing.

by Dn_Ab 14y ago

ten_fingers 14y ago
Trig? Fourier series and its introduction to functional analysis and Hilbert space and the ideas of inner products and orthogonality there. JPG image compression. Shannon's information theory. Characterization of time invariant linear systems, e.g., acoustics. Antenna theory. Phased arrays and beam forming. Imaging in optics. Holography. The fast Fourier transform. Seismic data analysis via the fast Fourier transform. Characteristic functions and Bochner's theorem. Power spectra. X-ray crystallography. The fundamental theorem of interpolation and the Nyquist sampling theorem (e.g., how music CDs work). There's a cute idea to put 100 wireless customers all on the same wavelength. Basically have a tricky antenna pattern with a lobe for each user and so that each user gets only their own signal. It's all trig.
- Dn_Ab 14y ago
  Indeed, I agree. Those all fall under the umbrella I gave. But those are all particular subject areas that many people can go through their career without touching.
  - ten_fingers 14y ago
    > Those all fall under the umbrella I gave. Yes, all or nearly all! That the trig functions are the source of the most important orthogonal basis in Hilbert space theory need not be good to know just for physics or signal processing! Let's see: Also I mentioned characteristic functions and Bochner's theorem which are core probability and not just physics or signal processing. Characterization of time invariant linear systems might be in mechanical engineering and might be tried even in economics! Seismic data analysis via the fast Fourier transform is, yes, in signal processing but is also mostly regarded as geology or just looking for oil or anything 'down there'. I tried, as you can see, I really tried, to show how trig was for more than just your father's topics in physics and signal processing. I tried!

I think the surprising commonality is conditional. So you won't see it unless you are focusing on physics or signal processing.

by Dn_Ab 14y ago

I think the surprising commonality is conditional. So you won't see it unless you are focusing on physics or signal processing.

ten_fingers 14y ago

Trig? Fourier series and its introduction to functional analysis and Hilbert space and the ideas of inner products and orthogonality there. JPG image compression. Shannon's information theory. Characterization of time invariant linear systems, e.g., acoustics. Antenna theory. Phased arrays and beam forming. Imaging in optics. Holography. The fast Fourier transform. Seismic data analysis via the fast Fourier transform. Characteristic functions and Bochner's theorem. Power spectra. X-ray crystallography. The fundamental theorem of interpolation and the Nyquist sampling theorem (e.g., how music CDs work). There's a cute idea to put 100 wireless customers all on the same wavelength. Basically have a tricky antenna pattern with a lobe for each user and so that each user gets only their own signal. It's all trig.

Dn_Ab 14y ago
Indeed, I agree. Those all fall under the umbrella I gave. But those are all particular subject areas that many people can go through their career without touching.
- ten_fingers 14y ago
  > Those all fall under the umbrella I gave. Yes, all or nearly all! That the trig functions are the source of the most important orthogonal basis in Hilbert space theory need not be good to know just for physics or signal processing! Let's see: Also I mentioned characteristic functions and Bochner's theorem which are core probability and not just physics or signal processing. Characterization of time invariant linear systems might be in mechanical engineering and might be tried even in economics! Seismic data analysis via the fast Fourier transform is, yes, in signal processing but is also mostly regarded as geology or just looking for oil or anything 'down there'. I tried, as you can see, I really tried, to show how trig was for more than just your father's topics in physics and signal processing. I tried!