The Bell 103 modem spec gives the following frequencies to use:

Transmit Side: 1070Hz (space) and 1270Hz (mark)

Receive Side: 2025Hz (space) and 2225Hz (mark)

Why were these specific frequencies chosen other than needing to fit into the voice band?

  • 3
    I can’t say definitively but frequencies will be chosen so that they don’t share harmonics with other often-used PSTN tones and AC power. Higher frequencies typically allow higher data rates, especially if crude modulation methods are used.
    – Frog
    Apr 28 '21 at 6:41
  • The bell 103 modem used Frequency Shift Keying modulation, which is about as crude as it gets. Normally with FSK methods, the frequencies are chosen to be even multiples of the bit rate so that the switching is smooth but that is not the case here.
    – Ben Longo
    Apr 28 '21 at 8:22
  • But in that case you’d want the IF (rather than the carrier) to be a multiple of the bit rate, would you not? Here the frequency shift is 200Hz. It seems strange that a bigger frequency shift wasn’t chosen, but perhaps that’s to keep the bandwidth low in the IF domain so it doesn’t encroach on the carrier. Put another way, an instantaneous switch from 1070 to 1270Hz will generate high-frequency energy. A gradual switch over 5ms (one IF cycle) will generate energy up to 400Hz, well below the carrier, so data going in one direction won’t interfere with data the other way.
    – Frog
    Apr 28 '21 at 9:59
  • Interestingly, it was not discussed in the Bell System Technical Journal until after the 103 modem was released in 1962. There is a good paper from 1968 for a digital design of this modem, but it does not clarify where these magic frequencies came from.
    – DrSheldon
    Apr 28 '21 at 14:39

Why were these specific frequencies chosen other than needing to fit into the voice band

Erm, in the end it's all about fitting in the voice band of 300..3400 Hz.

For one, 1 kHz and 2 kHz are almost equally spaced within the voice band, having the maximum distance between each and its boundaries, giving optimal placement and separation.

Next, 200 Hz between the signals each side can produce is small enough to not interfere (much) with the other side, while at the same time far enough apart to allow reliable discrimination with simple circuitry.

Last one (well, for here) is to keep harmonics down or far out. Far out is the best way, as filters tend to eliminate best signals that are way outside the passing window. I.e. as further out, as more energy is needed to get a signal thru. While this does not matter much on subscriber lines, it does on long distance (exchange to exchange) transmissions, as here single voice channels get multiplexed - saving a lot of copper. A technology already pioneered in the late 1930.

At that point we must take a step back and notice that the telephone network was made for speech and handling one channel. So there can not be specific filters for modem, but only for the whole channel. The analogue fall of of filters isn't much of an issue with regular audio. It becomes one with narrow band signals like modems create. Their frequencies are as well quite defined, thus harmonics carry more power, thus being harder to be cancelled out.

So, as so often in life it's about finding a middle ground among many parameters.

  • 1
    I find it somewhat curious that the upper frequency band includes the second harmonic of the lower frequency in the lower band. I would think a common way to construct a modem's receive stage would be to use a bandpass filter followed by a zero-crossing detector and pulse-width detector, but the second harmonic of 1070Hz (2140Hz) would pass through a 200Hz wide bandpass filter centered around 2125Hz better than would the actual frequencies of interest.
    – supercat
    Apr 28 '21 at 16:02
  • 2
    This all seems correct, but still doesn’t provide any specific motivation for the chosen frequencies other than “about 1k and 2k”
    – Ben Longo
    Apr 28 '21 at 17:37
  • @BenLongo Well, there is more than just the first paragraph.
    – Raffzahn
    Apr 28 '21 at 17:43
  • Why 2125Hz±100Hz rather than larger separation? It's only less than 5% of drift allowance.
    – Schezuk
    Nov 4 '21 at 7:59
  • @Schezuk Not sure what you mean. there is no 2125 Hz. Only 2025 and 2225 while separation is 200 Hz. Most important, when this is about keeping both transmission channels as far apart as possible, while keeping as well enough distance between them and the margins of the phone channel. so it's ~700/200/800/200/700.
    – Raffzahn
    Nov 4 '21 at 9:47

One consideration of the 2025/2225 frequencies (answer side sending tones) was that these turned off the echo suppressors on long distance lines. I suspect that the choice for the originate side tones was to be a reasonable distance frequency wise from the answer tones to easily be filtered, and not harmonically related.

The choices for the individual tones for touch-tone (DTMF) frequencies was possibly governed by these factors as well.

Sometimes they pick things that are "easy to do" and go from there.

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