Optimum Binary Signal One Can Transmit on a 1 Hz Frequency

Claude Shannon would certainly be able to shed some light on this subject. I suggest looking at some of his writings.

Kulas,

Why are you posing these types of questions here. You're smart enough to search the internet first... RIGHT???

Google search - "What's could be the equation limiting data transmission per Hz" - About 3,140,000 results (0.70 seconds)

I'm partial to insane clowns myself. By nature they are so much less predictable.

"Considering all possible multi-level and multi-phase encoding techniques, the Shannon-Hartley theorem states the channel capacity C, meaning the theoretical tightest upper bound on the information rate (excluding error correcting codes) of clean (or arbitrarily low bit error rate) data that can be sent with a given average signal power S through an analog communication channel subject to additive white Gaussian noise of power N, is:

where

C is the channel capacity in bits per second;
B is the bandwidth of the channel in hertz (passband bandwidth in case of a modulated signal);
S is the average received signal power over the bandwidth (in case of a modulated signal, often denoted C, i.e. modulated carrier), measured in watts (or volts squared);
N is the average noise or interference power over the bandwidth, measured in watts (or volts squared); and
S/N is the signal-to-noise ratio (SNR) or the carrier-to-noise ratio (CNR) of the communication signal to the Gaussian noise interference expressed as a linear power ratio (not as logarithmic decibels)."

https://en.wikipedia.org/wiki/Shannon%E2%80%93Hartley_theorem

https://en.wikipedia.org/wiki/Symbol_rate

https://en.wikipedia.org/wiki/Nyquist_rate

So, the answer is 42?

Wow, say B=1 & S/N=1 or SNR typical.

C= 1 log₂ (2) = 1 bit per second/1Hz. Nice, what if the wave is still modulated?

Anyhow what's the usual SNR? I mean range, @ normal conditions?

Why are you people responding to a question that is jibberish?

"Typically not a homework question. "

What about this time?

Once upon a time....

A rookie electronics engineer had to answer the question: how much information can you send on a marine band (some 4 MHz carrier) if you are constricted to 10 channels, each of 300 Hz bandwidth. He was full of...confidence, and answered that 300 Hz bandwidth will limit very much. There was this mid aged EE who told him that, if not constrained by time, and if he has enough precise transmitting and receiving devices, he can cast as much information he wanted. It is the rate of change of one of the three (amplitude, frequency or phase) that limits (talking ideal situations with no noise).

But that was a long, long time ago....

"10 channels, each of 300 Hz bandwidth"

You could send quite a lot. You could even have a secured communication, breaking the data up so each 8-bit byte gets spread across eight channels, with one channel sending the 'interleave' key for that packet⁽¹⁾ and one channel sending gibberish to confound hacking attempts.

Or am I getting too clever for the NSA's good? (Like you guys haven't seen that before, having fun reading everyone's e-mail, Agent? If you still have some air-sick bags to fill up, I could find the REALLY weird stuff to e-mail to myself.)⁽²⁾

Notes:

1. Say Interleave code 0x07 = 35296418 Yes, the 'gibberish channel' changes for every packet.
2. The way the NSA's been snooping, you don't think they're watching this forum as well?