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I've been playing with DTMF frequencies and the Goertzel algorithm, and would like to know exactly HOW the DTMF frequencies were determined. I understand that they were chosen such that none of the frequencies would be equal to sum and difference frequencies, or intermodulation products, but I can't find any information on whether the frequencies were simply determined through experimentation, mathematical calculation, etc… does anyone know more about this?

Also, I would like to understand how to extend the two sets of frequencies to two sets of 8 frequencies, or 3 sets of 4 frequencies, such that it's possible to represent 64 keys. I'm not sure whether it would be easier to work with 3 sets of 4 versus 2 sets of 8 each. I guess the analysis would be easier if just using 2 sets of 8? There would be less intermodulation products to keep in mind …

Thanks! B

EDIT: if it's too difficult to track back how this was achieved, i would like to know what the best way is to find 2 sets of frequencies, giving 64 unique combinations, and such that if you pick 2 frequencies from each of the 2 sets randomly, and mix the sine waves together, and put them through some non linear distortion, they are still easily detectable using goertzel, and the other frequencies are not "hit" (their bins remain at a normal background noise level)

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  • $\begingroup$ Perhaps someone who worked on the original Touch-Tone spec would know. Otherwise, you may need to find some obscure ATT memos or such. And there is info in other sources ( eg: repeater-builder.com/tech-info/dtmf/dtmf.html or: nemesis.lonestar.org/reference/telecom/signaling/dtmf.html ) $\endgroup$ – Kevin McGee Dec 3 '13 at 3:19
  • $\begingroup$ As noted in the first link above: 1) TouchTone was designed to fit an 8x8 matrix, and 2) the frequencies follow a 21/19 ratio. $\endgroup$ – Kevin McGee Dec 4 '13 at 4:24
  • $\begingroup$ @KevinMcGee I checked the above links but did not see an 8x8 matrix? $\endgroup$ – b20000 Dec 4 '13 at 5:13
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    $\begingroup$ The author states: "And it's not common knowledge that the tone matrix is larger than four rows and four columns. If you extend the tone mathematical sequence (it's a 21/19 ratio) it works out to an 8 by 8 matrix. Yes, the Bell System / Western Electric engineers designed the Touchtone matrix to fit 64-buttons into the voice band and only the top left corner was ever implemented." $\endgroup$ – Kevin McGee Dec 4 '13 at 17:08
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From page 293 of Engineering and Operations in the Bell System (1982-1983) by AT&T Bell Labs:

The tones have been carefully selected to minimize harmonic interference and the probability that a pair of high and low tones will be simulated by the human voice, thus protecting network control signaling.

P.S. Yes, I know this answer is 6 years late, I just happened to be researching for the answer and I thought this could help.

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See Bell System Technical Journal 39: 1. January 1960: Pushbutton Calling with a Two-Group Voice-Frequency Code. (Schenker, L.).

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