Can the Signal from a Coaxial Cable be Transmitted via Bluetooth?
(Expanding on Kurt E Clothier's comment ...)

As often, the answer should be "it depends", in this case on the nature of the signal that's being transmitted via the coax cable. If the original signal is an analog type signal this type of transmission would involve several steps:


Conversion of the analog signal into digital byte stream using an analog-to-digital converter (=ADC), most likely with a little bit of pre-amplification of the signal.
Packaging and transmission of the digital signal via the Bluetooth transmitter to the Bluetooth receivers.
Back-conversion of the received digital signal into an analog signal using a digital-to-analog converter (=DAC), again followed by some signal conditioning.


As you can imagine, these steps all take some time. The ADC can only convert the analog signal to digital bytes a finite number of times per second (the so-called sampling rate). Similarly, the Bluetooth radios (transmitter and receivers) can only transmit a finite number of bits/bytes per second. Lastly, the DAC can only convert so many samples per second back into analog form. Therefore, if your original signal doesn't change very quickly (the 20 Hz you mention would not be considered quick at all), all the steps have enough time to complete. If it is changing more quickly, there simply isn't enough time to complete the different steps.

Another thing that follows from the description above is that with each conversion between analog and digital domain, the signal will be altered just a little bit. Both your ADC and your DAC have limited "resolution" (e.g. 8-bit, 10-bit, 16-bit ...), with higher resolution meaning that the ADC can produce a more fine-grained representation of the signal (see Quantization. Again, it depends on the nature of your original signal whether the small alterations done during the conversion steps are tolerable or not.