3 ms·

so, hold on, he's wanting to charge people $10 (to get a file) to attempt to solve the problem, then give a prize of $1000 to anyone who can do it? Hmmm. Inte

so, hold on, he's wanting to charge people $10 (to get a file) to attempt to solve the problem, then give a prize of $1000 to anyone who can do it? Hmmm. Interesting.

fellellor 9y ago
He does provide a Jupyter notebook to try out your preliminary ideas. From what I've seen people in the DSP community are very anal about the inviolability of the sampling theorem. So charging $10 may be his way to punish novice "fools" who think they know better. I'm not sure I disagree.
- enriquto 9y ago
  If you understand the sampling theorem, its meaning is self-evident, you just count the degrees of freedom. Ask a mathematician how many samples do they need to recover the coefficients of a polynomial of degree 10. They will say: 11 samples are necessary and sufficient, if you have less than 11 samples then you cannot recover any coefficient. If you have 11 or more samples you can recover all the coefficients. The sampling theorem is exactly the same thing but for trigonometric polynomials.
  - tmuir 9y ago
    I don't understand it from this angle, but to me, the general description of what they employ sounds very analogous to how noise cancelling headphones work for pilots. The noise generated by the engines, which normally would drown out any signal of humans conversing through air, is of known frequencies, and a synthesized version of that noise can be played back 180 degrees out of phase along with the original audio, cancelling the noise, revealing the signal. No one is implying that the headphones do this without sampling the engine noise, they might just not have to rely on the actual measurements in question to glean the necessary information to synthesize a signal capable of such cancellation. It reads to me like this broadband thermal noise is predictable, which is why they are able to synthesize it in the first place.
    - enriquto 9y ago
      The statement of sampling theorem has nothing to do with noise. It only states that there is conservation of information.
      - tmuir 9y ago
        You misunderstood. I was relaying that I, too, have a decent grasp of sampling theory, and that if I understand the article's main premise, then saying they have disproven Nyquist's Theorem with this example is akin to saying that being able to draw both 30 degree and 90 degree angles with a compass disproves the idea that angle trisection is generally impossible. They have simply shifted in time the sampling of the noise. Even if they argue they synthesize the noise in realtime, they had to have sampled it at some point to know what to synthesize in the first place. It was at this point that they were required to sample at at least 2MHz to accurately quantify their noise at 1MHz. The mechanism used in pilot's noise cancelling headphones is much the same. they don't sample the engine noise as its being made, they synthesize it from known frequencies.
photojosh 9y ago
The $10 is a filter to avoid people wasting his time. Anyone with knowledge in signal processing would be able to generate their own test data sets from the description.
seba_dos1 9y ago
The problem is entirely solvable without the file (if there's really a solution, that is). If you believe you have solved the problem, you will surely pay $10 to get the file so you can prove it and get $1000.

so, hold on, he's wanting to charge people $10 (to get a file) to attempt to solve the problem, then give a prize of $1000 to anyone who can do it? Hmmm. Interesting.

fellellor 9y ago

He does provide a Jupyter notebook to try out your preliminary ideas. From what I've seen people in the DSP community are very anal about the inviolability of the sampling theorem. So charging $10 may be his way to punish novice "fools" who think they know better. I'm not sure I disagree.

enriquto 9y ago
If you understand the sampling theorem, its meaning is self-evident, you just count the degrees of freedom. Ask a mathematician how many samples do they need to recover the coefficients of a polynomial of degree 10. They will say: 11 samples are necessary and sufficient, if you have less than 11 samples then you cannot recover any coefficient. If you have 11 or more samples you can recover all the coefficients. The sampling theorem is exactly the same thing but for trigonometric polynomials.
- tmuir 9y ago
  I don't understand it from this angle, but to me, the general description of what they employ sounds very analogous to how noise cancelling headphones work for pilots. The noise generated by the engines, which normally would drown out any signal of humans conversing through air, is of known frequencies, and a synthesized version of that noise can be played back 180 degrees out of phase along with the original audio, cancelling the noise, revealing the signal. No one is implying that the headphones do this without sampling the engine noise, they might just not have to rely on the actual measurements in question to glean the necessary information to synthesize a signal capable of such cancellation. It reads to me like this broadband thermal noise is predictable, which is why they are able to synthesize it in the first place.
  - enriquto 9y ago
    The statement of sampling theorem has nothing to do with noise. It only states that there is conservation of information.
    - tmuir 9y ago
      You misunderstood. I was relaying that I, too, have a decent grasp of sampling theory, and that if I understand the article's main premise, then saying they have disproven Nyquist's Theorem with this example is akin to saying that being able to draw both 30 degree and 90 degree angles with a compass disproves the idea that angle trisection is generally impossible. They have simply shifted in time the sampling of the noise. Even if they argue they synthesize the noise in realtime, they had to have sampled it at some point to know what to synthesize in the first place. It was at this point that they were required to sample at at least 2MHz to accurately quantify their noise at 1MHz. The mechanism used in pilot's noise cancelling headphones is much the same. they don't sample the engine noise as its being made, they synthesize it from known frequencies.

photojosh 9y ago

The $10 is a filter to avoid people wasting his time. Anyone with knowledge in signal processing would be able to generate their own test data sets from the description.

seba_dos1 9y ago

The problem is entirely solvable without the file (if there's really a solution, that is). If you believe you have solved the problem, you will surely pay $10 to get the file so you can prove it and get $1000.