For fun and no real practical use, I'm trying to design a DIY modem that can transmit data over an audio line, like old 56k modems did. I'm studying how to pack bits of data efficiently in a 1k-15k audio spectrum, such that I'll be able to de-modulate it later.
During my readings, I saw that DSL modem use the 25 kHz – 1 MHz spectrum, in order to avoid interference with voice on the telephone line.
Question: on the demodulation side, in order to be able to do digital signal processing (FFT, etc.) to identify peaks of spectrum at, say 400 kHz or 800 kHz or 1 MHz, one needs a 2 MHz sampling rate (Nyquist).
Do (A)DSL modems have ADC (analog to digital converters) with 2 MHz sampling rate?
Same question for dial-up 56k modems: what kind of sampling frequency did they use at the ADC/DAC stage?
Best Answer
They have a much faster ADCs. Also, ADSL2+ has its downlink up to maybe 2.2 MHz, so you'd need at least 4.4 MS/s to do that.
In reality, single-digit MHz ADCs are "old tech" and relatively cheap. Together with it being desirable to oversample the signal to apply digital filtering to increase your SNR, I'd presume that modern (as in: of the last 20 years!) ADSL modems have > 5 MS/s ADCs.
You'll probably not find a separate ADC on the board – typically, these things are integrated into AFE (analog front-end) ICs, integrating both ADC as well as DAC and a fair bit of analog and digital signal conditioning, and usually things like digital downconversion, sometimes clock recovery.
Such chips make highly-integrated and cheap DSL modems possible, but also make these devices less useful as general-purpose ADCs.
Also, because you ask like that, and because people will wonder anyway: No. This is not a clever way to circumvent export restrictions / technology embargoes. Officials in charge of export control aren't stupid, and companies want to sell millions of chips for DSL modems everywhere, so I'd assume it'll be practically impossible for the average engineer to convert these to general purpose ADCs/DACs.