Do DSL / ADSL modems have an ADC with ~ 2 MHz sampling rate?

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?

• The H in Hz is supposed to be capitalized, by the way. Because it is someone's name. – DKNguyen Sep 27 '20 at 19:23
• @BrianDrummond Do you mean, as high? Typical ADC/DAC I've seen for DSP have between 8 kHz and 100 kHz sampling-rate. Are there 2 mHz DAC/ADC easily available? – Basj Sep 27 '20 at 19:40
• @Basj lol, are you a time traveller from the 1970s? You can buy Gigasample/s ADCs on the free market... Every mid-range MCU has a > 1MS/s ADC, these days. – Marcus Müller Sep 27 '20 at 19:42
• @MarcusMüller Oops this might be because I've always worked with audio signals, so typical DACs I used were 8 / 16 / 48 / 96 / 192 kHz, with 24 bit resolution :) Outside of the audio world, what are typical DACs since, say 2000? Is a 1 Mhz DAC with 16 bit resolution something common? – Basj Sep 27 '20 at 19:45
• It's "MHz" and "GHz, not "mHz", "Mhz" or "Ghz". Capitals matter! Tip: SI units named after a person have their symbols capitalised but are lowercase when spelt out. – Transistor Sep 27 '20 at 19:56

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.

• Not to mention that DSLs like ADSL, HDSL, etc., do something else -- they separately monitor on the order of 1000 (256 in ADSL, memory serving) individual frequency bands for their $Z_\text{LOAD}$ and actively optimize their $Z_\text{DRIVE}$ to maximize transmission performance, band by band, in real-time. Copper telephone lines are notoriously bad environments for data transfer (though they are well-equipped to handle lightening events at both ends.) – jonk Sep 27 '20 at 21:22
• I have never heard before of export restrictions on ADCs. Are you referring to something specific, or just speaking generally? – Nonny Moose Sep 28 '20 at 22:47

ADSL modems were usually >2Msps, often a multiple of 1.1Msps to simplify the signal processing later. E.g. the MTC20174 ADSL analog frontend had a 8.8Msps ADC/DAC. The reason for the higher than necessary sampling rate was the use the higher sampling rate to get more effective bits at signal frequency. This is a quite common trick as increasing sampling rate is often easier than reducing sampling noise in ADCs.

56k modems are ... special. They operated in an asynchronous fashion, something which ADSL later copied. They offered 56kbit/s down, but only 33.6kbit/s up. The reason of this lies in how they cheated. Back in the days of old, ISDN was considered the future and people who wanted to stay with current technology, upgraded to ISDN. ISDN could deliver two times 64kbit/s (plus a 16kbit/s signaling channel). Now to have ISDN available for customers, the whole telephone network has to support ISDN, or in other words has to be digital. V90 made use of that in that it knew the analog path in the connection was only that between the central and the last mile to the customer. The rest was digital. So, if your ISP had the equipment to interface digitally, they could inject digital samples into the phone network, which would be transmitted digitally until it reached the last central. This way it was possible to make use of the 64kbit/s that ISDN networks boasted, as you could, sample by sample transmit the analog signal and almost 100% recover it at the receiver end, as the analog wire was really short. The "encoding" used was simple PAM at the 8ksps / 8bits/sample that ISDN featured. But as signal noise and ADC/DAC linearity was far from offering perfect conditions, only 7bit of the 8bit samples were used. ADC/DACs used in these modems were usually 64ksps and 128ksps with 8bit (we are talking about the second half of the 90s, so these were state of the art chips that didn't cost an arm and a leg and could be used in a modem that should cost less than \$200).

So, why was this only used down stream? Because the receiver had to be synchronized to the sender. While it was possible to add a synchronizer (aka clock recovery and PLL) to the modem, nobody would have paid for the changes in telephone infrastructure to synchronize them. So upstream was still V34bis with its QAM.