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I'm talking about a continuous analog channel.

  • Why can't it support infinite bandwidth?
  • Is there a physics reasons for it say for electrical signals?
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  • $\begingroup$ i think a physical reason for finite bandwidth has something to do with the non-zero mass of the electron, so the charge-to-mass ratio is finite, and that the speed of light (which is the speed of the EM interaction) is finite. $\endgroup$ – robert bristow-johnson Apr 6 '17 at 2:37
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Information bandwidth is dependent on signal to noise ratios. At absolute zero, quantum level signal quantization and quantum noise will limit the lower bound on the noise floor. At higher temperatures, thermal noise creates a higher noise floor in any information receiving equipment. There may also be an upper limit on power density in a signal before its mass equivalent creates a black hole, which may be problematical in terms of information conservation. In terms of transmitters, at some point you will melt the wires.

But in terms of pure math, there is no (aleph zero) finite limit on the amount of information that a single real number (one sample) can contain.

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    $\begingroup$ True: A real number contains the Universe $\endgroup$ – Laurent Duval Apr 4 '17 at 21:30
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    $\begingroup$ @LaurentDuval may be an irrational number (which is of coure also real anyway), but otherwise 2.0 , being a real, not so much contains the universe... $\endgroup$ – Fat32 Apr 5 '17 at 18:47
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    $\begingroup$ Depends on which number basis. 2.0 in the $\phi$ basis may do it :) $\endgroup$ – Laurent Duval Apr 5 '17 at 19:05
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In addition to hotpaw2's answer, attempting to increase the bandwidth by increasing the frequency range will also fail at some point. The impedance of a capacitor is given by

Z = 1 / (2 π f C)

where f is the frequency and C the capacitance. Any two bits of metal separated by an insulator form a capacitor. As the frequency increases towards infinity, the impedance tends towards zero. In other words, every bit of metal in your circuit ends up shorted to every other bit of metal. At that point, it becomes impossible to generate the signal in the first place.

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