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Orthogonality is a beautiful concept. In physics, different frequencies don’t interfere with each other—they're always independent. However, in digital operati

Orthogonality is a beautiful concept. In physics, different frequencies don’t interfere with each other—they're always independent. However, in digital operations and mathematics, this isn’t automatically true, so we need to carefully select the right frequencies. OFDM leverages this by ensuring that, in the frequency domain, certain frequencies remain completely separate, meaning changes to one frequency (in amplitude or phase) won't affect the others. This allows us to capture the maximum information with limited samples.

jjtheblunt 2y ago
> In physics, different frequencies don’t interfere with each other—they're always independent. Are you overlooking harmonics? Are you overlooking the same frequency case of noise cancellation, via phase shift?
- layer8 2y ago
  Phase shift isn’t different frequencies?
  - jjtheblunt 2y ago
    Please check out the 3rd paragraph of this article. https://en.wikipedia.org/wiki/Active_noise_control https://en.wikipedia.org/wiki/Active_noise_control
    - layer8 2y ago
      I’m aware of how ANC works. It uses the same frequencies with reverse amplitude. The comment you objected to however was talking about different frequencies.
      - 01HNNWZ0MV43FF 2y ago
        > reverse amplitude Right? One of my dumb noobie questions has always been why textbooks explain ANC as "180 phase shift" instead of "reverse amplitude". Do they really do an entire DSP pass to break apart a signal and phase-shift it just to get the output that a minus sign could get? There must be something missing from the plum-pudding model.
        itishappy 2y ago
        It's only a sign flip when the detector and emitter are perfectly in phase. Adding delay causes the required phase shift will drift slightly. Also note that the phase offset of a delay is frequency dependent, so this drift will be as well. Another reason is that devices and materials have different frequency responses, so an external signal needs to be filtered to match the levels in the device.
  - jjtheblunt 2y ago
    I wasn't clear : phase shift has a clear example: think of two sine waves, one whose value at time t is sin(t) and the other sin(t+pi/2). they'd have the same period, and frequency, but would be phase shifted by that addition in the time parameter. Here's a graphed example. https://www.wolframalpha.com/input?i=Plot%5BSin%5Bt%5D%2CSin%5Bt%2B1.57%5D%5D https://www.wolframalpha.com/input?i=Plot%5BSin%5Bt%5D%2CSin... For another fun example, here's the residential power in current American homes: two 120v A/C feeds, out of phase so that you can combine them in the breaker box to get 240v A/C. https://www.wolframalpha.com/input?i=Plot%5B120*Sin%5Bt%5D%2C120*Sin%5Bt%2B3.1415%5D%5D https://www.wolframalpha.com/input?i=Plot%5B120*Sin%5Bt%5D%2...
- nakulgarg22 2y ago
  You're correct - I oversimplified assuming no doppler effect and a linear time invariant system. The key is that we can still analyze and manipulate frequency components independently in REAL PHYSICAL WORLD, which enables techniques like OFDM.

jjtheblunt 2y ago

> In physics, different frequencies don’t interfere with each other—they're always independent. Are you overlooking harmonics? Are you overlooking the same frequency case of noise cancellation, via phase shift?

layer8 2y ago
Phase shift isn’t different frequencies?
- jjtheblunt 2y ago
  Please check out the 3rd paragraph of this article. https://en.wikipedia.org/wiki/Active_noise_control https://en.wikipedia.org/wiki/Active_noise_control
  - layer8 2y ago
    I’m aware of how ANC works. It uses the same frequencies with reverse amplitude. The comment you objected to however was talking about different frequencies.
    - 01HNNWZ0MV43FF 2y ago
      > reverse amplitude Right? One of my dumb noobie questions has always been why textbooks explain ANC as "180 phase shift" instead of "reverse amplitude". Do they really do an entire DSP pass to break apart a signal and phase-shift it just to get the output that a minus sign could get? There must be something missing from the plum-pudding model.
      - itishappy 2y ago
        It's only a sign flip when the detector and emitter are perfectly in phase. Adding delay causes the required phase shift will drift slightly. Also note that the phase offset of a delay is frequency dependent, so this drift will be as well. Another reason is that devices and materials have different frequency responses, so an external signal needs to be filtered to match the levels in the device.
- jjtheblunt 2y ago
  I wasn't clear : phase shift has a clear example: think of two sine waves, one whose value at time t is sin(t) and the other sin(t+pi/2). they'd have the same period, and frequency, but would be phase shifted by that addition in the time parameter. Here's a graphed example. https://www.wolframalpha.com/input?i=Plot%5BSin%5Bt%5D%2CSin%5Bt%2B1.57%5D%5D https://www.wolframalpha.com/input?i=Plot%5BSin%5Bt%5D%2CSin... For another fun example, here's the residential power in current American homes: two 120v A/C feeds, out of phase so that you can combine them in the breaker box to get 240v A/C. https://www.wolframalpha.com/input?i=Plot%5B120*Sin%5Bt%5D%2C120*Sin%5Bt%2B3.1415%5D%5D https://www.wolframalpha.com/input?i=Plot%5B120*Sin%5Bt%5D%2...
nakulgarg22 2y ago
You're correct - I oversimplified assuming no doppler effect and a linear time invariant system. The key is that we can still analyze and manipulate frequency components independently in REAL PHYSICAL WORLD, which enables techniques like OFDM.