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Practically speaking, how would you use a continuous Fourier transform? Do you mean passing it through a "Fourier transform analog circuit" (does that even exis

Practically speaking, how would you use a continuous Fourier transform? Do you mean passing it through a "Fourier transform analog circuit" (does that even exist?), and then sample the output?

taeric 7y ago
I was curious on this. Still am. Tried thinking of several things it could mean, but so far I'm coming up short.
- radarsat1 7y ago
  I think what he means is that in signal processing you can define the signal analytically and perform the Fourier transform analytically, without sampling. The Nyquist rate only comes in when you talk about digital signal processing.
  - mlazos 7y ago
    This was what I meant initially, but I realized in a lot of NNs that it might be pretty difficult if not impossible to define the signal analytically.
    - taeric 7y ago
      Ah, if I take your meaning of analytically correctly, I think you are basically arguing for symbolic reasoning. I do still see the appeal of that. Seems solidly not a promising path, at this point. :(
mlazos 7y ago
See my other answer - I meant applying it analytically. Your idea is interesting though, and I do know that it should be possible to build a Fourier transform analog circuit. Once you sample though you will be subject to having a nyquist frequency and introducing noise to your signal and the advantage of performing it with an analog circuit will be lost.
- funklute 7y ago
  Yea, actually I thought a bit more about it as well, and any real (analog) circuit will have a frequency response that tapers of to zero as the frequency goes to infinity. So that basically determines a Nyquist frequency for any analog circuit, even if that frequency is so high that it has no practical implications.
dreamcompiler 7y ago
Build a bank of bandpass filters with different center frequencies, and you have an analog Fourier transform. (Or at least the power spectrum equivalent; it's trickier to get the phase info.) Analog vocoders are one example of this and they were invented long before discrete FTs.

Practically speaking, how would you use a continuous Fourier transform? Do you mean passing it through a "Fourier transform analog circuit" (does that even exist?), and then sample the output?

taeric 7y ago

I was curious on this. Still am. Tried thinking of several things it could mean, but so far I'm coming up short.

radarsat1 7y ago
I think what he means is that in signal processing you can define the signal analytically and perform the Fourier transform analytically, without sampling. The Nyquist rate only comes in when you talk about digital signal processing.
- mlazos 7y ago
  This was what I meant initially, but I realized in a lot of NNs that it might be pretty difficult if not impossible to define the signal analytically.
  - taeric 7y ago
    Ah, if I take your meaning of analytically correctly, I think you are basically arguing for symbolic reasoning. I do still see the appeal of that. Seems solidly not a promising path, at this point. :(

mlazos 7y ago

See my other answer - I meant applying it analytically. Your idea is interesting though, and I do know that it should be possible to build a Fourier transform analog circuit. Once you sample though you will be subject to having a nyquist frequency and introducing noise to your signal and the advantage of performing it with an analog circuit will be lost.

funklute 7y ago
Yea, actually I thought a bit more about it as well, and any real (analog) circuit will have a frequency response that tapers of to zero as the frequency goes to infinity. So that basically determines a Nyquist frequency for any analog circuit, even if that frequency is so high that it has no practical implications.

dreamcompiler 7y ago

Build a bank of bandpass filters with different center frequencies, and you have an analog Fourier transform. (Or at least the power spectrum equivalent; it's trickier to get the phase info.) Analog vocoders are one example of this and they were invented long before discrete FTs.