Transmitting on all frequencies?

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Transmitting on multiple frequencies simultaneously is feasible through various methods, including the use of driven LRC circuits and nonlinear devices like transistor amplifiers. While an ideal pulse theoretically comprises infinite frequencies, practical limitations prevent achieving it, though sharp impulses can approximate this effect. Harmonics and mixing products generated by nonlinear devices allow broadcasting across several frequencies at once. Ultra wideband modulation techniques further enable the transmission of multiple frequency sets through a single broadband antenna. Overall, the combination of these methods facilitates effective multi-frequency transmission.
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i know you've heard this in a movie or something, usually when a ship is sinking or the last survivor of the human race is looking for other survivors. considering a transmitter is just a driven LRC circuit oscillating at a certain frequency, is this possible? obviously you could have a bunch of different transmitters going at the same time or broadcast, change the frequency of oscillations and retransmit but could you broadcast on several freqs at once?
 
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An ideal pulse such as described by the dirac delta function is composed of infinite frequencies. You can check that by taking its Fourier transform.

But practically it's impossible to achieve an ideal pulse with infinite amplitude, and 0 period, but you can get a bit close.

Another way is to generate harmonics. By passing a radio signal through a nonlinear device such as a transistor amplifier, the output will be composed of the fundamental frequency and its multiples. Its possible to mess around with the nonlinear device to produce all kinds of subharmonics, and mixing products.
 
You can broadcast on several frequencies at once,
there's the Fourier transform relationship between a waveform and the frequencies that make up the waveform.

So in fact anything that isn't an infinite duration pure
sine wave occupies a spread of frequencies.

If you transmit very sharp impulses they'll cover a wide
range of frequencies, and the old "spark gap" transmitters
worked in just such a way to generate RF at some useful
frequency range without very precise control of oscillator
tuning in the transmitter.

To really cover a wide range of frequencies there are
"ultra wideband" modulation techniques. To cover
several sets of individual frequencies at once you can
just generate the waveform of each of those transmissions
and add them together coming out of one broadband
antenna.
 
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