DTMF stands for Dual-Tone Multi-Frequency. That is, a DTMF signal is one that consists of only the sum of two pure sinusoids at valid frequencies.  The picture below shows which two frequencies produce what tone.
                1209Hz 1336Hz 1477Hz 1633Hz
                  |      |      |      |
                 .-.    .-.    .-.    .-.
         697Hz -( 1 )--( 2 )--( 3 )--( A )
                 >-<    >-<    >-<    >-<
         770Hz -( 4 )--( 5 )--( 6 )--( B )
                 >-<    >-<    >-<    >-<
         852Hz -( 7 )--( 8 )--( 9 )--( C )
                 >-<    >-<    >-<    >-<
         941Hz -( * )--( 0 )--( # )--( D )
                 `-'    `-'    `-'    `-'

Anyway, in DTMF, the tone '8' is represented with the sum of 852 Hz and 1336 Hz sinusoids.  It is understood that the energy of the sinusoids present in the generated tone should exceed the energy present at any other frequencies by 30dB.  Also, the DTMF frequencies are effectively divided into two subsets. One contains the lower four frequencies, and the other contains the upper four.  Each DTMF tone is defined by the presence of exactly one of the frequencies from each of those subsets.

CCITT DTMF Recommendations

Frequency Tolerance:  Operation:     <= 1.5%
                      Non-Operation: >= 3.5%
Signal Duration:      Operation:     40ms max
                      Non-Operation: 23ms min
Signal Interruption:                 10ms max
Twist:                Normal:        8db max
                      Reverse:       4db max

Any frequency within 1.5% of the DTMF frequency should be detected. Frequencies with 3.5% error should never be detected.  Inside the 1.5% - 3.5% range is a don't care. DTMF signals lasting 40ms should always be detected.  Signals less than 23ms should never be detected. Inside the 23ms-40ms range is a don't care.  DTMF signals that are interrupted for 10ms or less should not detect two separate signals.  Twist is caused by a non-uniform power loss across the frequency spectrum.  Normal twist is when low frequency power is greater than high frequency. Reverse twist is obviously the reverse condition.  The detector must be reject 8db and 4db for normal and reverse twist respectively.

Another facet of the MF keypad is that it protects against mis-operation to the extent that, if two adjacent buttons are operated together, the frequencies not common to both will be suppressed.  The exchange will fail to recognise the digit. 

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Last revised: November 11, 2021