- #1
Jim Fowler
- 2
- 1
Hi,
I'm struggling with a conceptual problem involving the Fourier transform of distributions. This could possibly have gone in Physics but I suspect what I'm not understanding is mathematical.
The inverse Fourier transform of a Cauchy distribution, or Lorentian function, is an exponentially decaying sinusoid. What I don't get is this...
Can't I, in principle, play a sound through a speaker that has any frequency distribution I like? If I choose to continuously play such a sound with a Cauchy distribution of frequencies, what will I hear? Does the sound decay exponentially? If I'm continuously sending that combination of frequencies to my speaker, that doesn't make sense to me.
Any insights about what it is I'm missing would be most welcome.
Thanks in advance.
I'm struggling with a conceptual problem involving the Fourier transform of distributions. This could possibly have gone in Physics but I suspect what I'm not understanding is mathematical.
The inverse Fourier transform of a Cauchy distribution, or Lorentian function, is an exponentially decaying sinusoid. What I don't get is this...
Can't I, in principle, play a sound through a speaker that has any frequency distribution I like? If I choose to continuously play such a sound with a Cauchy distribution of frequencies, what will I hear? Does the sound decay exponentially? If I'm continuously sending that combination of frequencies to my speaker, that doesn't make sense to me.
Any insights about what it is I'm missing would be most welcome.
Thanks in advance.