DTMF Decoder

Press a key on a phone and you hear a chord. Two notes, slightly sour together, gone the moment you let go. It is one of the most carefully argued sounds of the last century.

Before the chord there was the click. A rotary dial signals by interrupting the direct current in the line: one break for a 1, ten for a 0, at a nominal ten pulses per second, with a gap of at least 400 milliseconds before the next digit. The timing suited the electromechanical switches the pulses had to drive. A zero costs a full second of clicking and then a wait. Worse, a pulse is an event in the current on one pair of wires. It reaches the local exchange and stops there.

On November 18, 1963, Bell Telephone began the first commercial push-button service, in Carnegie and Greensburg, Pennsylvania. The sets had ten buttons; the star and the hash arrived soon after. A key press takes a small fraction of the second a rotary zero needs, but speed was only half of it. Tones are sound, so they go wherever speech goes, and a caller can keep signaling after the call connects, to a person or a machine at the far end.

The four-by-four code

The design behind those buttons was set out by L. Schenker in the Bell System Technical Journal in January 1960. Its stated aim was to signal end to end, over any established connection that will transmit speech. That ambition created the central difficulty. A signal that lives in the voice channel shares it with voices, and a receiver listening for tones will sooner or later hear a talker produce them. Engineers named the failure talk-off: false signaling caused by speech or noise.

Schenker’s answer was a code he called four-by-four. Eight frequencies are split into a low group and a high group of four each, and every valid signal is one tone from each group, sounded together. Four times four gives 16 signals. A single tone would have been simpler, but signals with a simple structure are, in the paper’s words, prone to frequent imitation by speech and music. Two is the smallest count above one. Knowing that a real signal always has exactly two parts is itself a statistical advantage.

International standards fix the result. The low group, 697, 770, 852 and 941 Hz, marks the rows of the keypad. The high group, 1209, 1336, 1477 and 1633 Hz, marks the columns, so the whole system spans 697 to 1633 Hz. The top row reads 1, 2, 3, A and the bottom row reads star, 0, hash, D. The European transmitter standard holds a sender within 1.5 percent of each frequency, noting that the international recommendation allows 1.8, and wants all unwanted frequencies together at least 20 dB below the low tone.

Why those odd numbers

Nothing about 697 or 1336 looks designed, and that is the point. The 1960 paper explains that a vowel is a buzz from the vocal cords, a fundamental and a long series of harmonics, shaped into formants. Its spectrum is full of frequencies in simple whole-number ratios. So the pairs were placed to avoid such ratios; the paper names 1:2, 2:3, 3:4, 3:5, 4:5 and 5:6. The tones also had to fit between 700 and 1,700 cycles per second and stay far enough apart to be told apart when sets were accurate to about 1.5 percent. A ladder in which each tone is 21 : 19 times its neighbor met all of that.

The ladder is easy to check. Multiply 697 by 21 and divide by 19 and you get 770.4. From 770 the same step gives 851.1, and from 852 it gives 941.7. In the high group, 1209 gives 1336.3, 1336 gives 1476.6 and 1477 gives 1632.5. Now double the low tones: 1394, 1540, 1704, 1882. None lands on a high tone. No frequency in the set is a harmonic of another.

The high group printed in 1960 ran 1,094, 1,209, 1,336 and 1,477; the group in use today starts one rung up the same ladder and ends at 1633. The paper also admits the limit of its own trick. Of about 65 troublesome harmonic combinations it counted, 18 were not avoided. The frequencies make imitation unlikely. They do not make it impossible.

The code has sixteen signals, and the European standard lets a system use only ten of them, the digits, or twelve, with the star and the hash added. The other four, the column at 1633 Hz, hardly reached the public. Their best known use was military. AUTOVON, a United States military telephone system developed in 1963, labeled the extra keys FO, F, I and P, for flash override, flash, immediate and priority. A caller pressed one to be given a free line ahead of others. Later keypads call them A, B, C and D. Receiver chips still decode them, and one common chip has a pin whose only job is to ignore them.

How a receiver decides a tone is real

Generating the chord is easy. Deciding that you heard one is the hard part, and the European receiver standard spells out what a receiver must weigh: presence, accuracy, balance and time.

Presence means one and only one frequency from each group. Accuracy means a receiver must respond to a tone within 1.5 percent plus 2 Hz of nominal. The data sheet of one common receiver chip adds the other side: it rejects a tone that is 3.5 percent off.

Balance has its own word, twist: the difference in level between the two tones. A telephone line weakens high frequencies more than low ones, so the high tone tends to arrive fainter, and Schenker’s design sent it 3 dB stronger to compensate. The European transmitter standard still asks for the high tone to leave 1 to 4 dB stronger. Its receiver standard requires a difference of up to 6 dB to be accepted, and the common chip accepts 8 dB either way.

Time is the strongest test. The European receiver standard requires a tone lasting more than 40 ms to be accepted and one shorter than 20 ms to be ignored. A break of less than 20 ms inside a tone must not split it in two, and a new digit must follow more than 40 ms without a valid signal. The longer a receiver waits, the less likely speech is to hold two exact frequencies steady throughout. The 1960 paper had already settled on a recognition time of the order of 40 milliseconds.

In software the usual tool is the Goertzel algorithm. A fast Fourier transform computes every frequency bin at once, and a keypad needs eight. Goertzel computes one bin with a short recursion on each sample, which makes it the efficient choice when only a few frequencies matter. The cost is a choice of block length. Bin width is the sample rate divided by the number of samples, so 100 samples at 8 kHz give bins 80 Hz wide, too coarse to separate 697 from 770. A MathWorks example uses 205 samples, or 25.6 ms.

How well does all this work? Never perfectly. The European standard asks for no more than 46 false operations in 100 hours of speech. Its shorter test is a 20 minute sequence distilled from 10 hours of speech in at least four languages, with female and male voices, on which no more than 5 false operations may occur. These are budgets for failure, written by people who knew that some vowel, somewhere, will always sound like a 5.

Where the tones went

The chord outlived the network it was built for. It is how a caller answers a recorded menu: the internet standard that carries keypad digits notes that the device consuming them is most commonly an interactive voice response system. Radio amateurs whose transceivers can produce the tones use them to place telephone calls through a repeater’s autopatch. The data sheet for a common receiver chip lists paging systems, mobile radio repeaters, credit card systems, remote control and answering machines.

On internet calls the sound itself is often missing. Codecs that squeeze speech into few bits are built to predict a voice, not a pair of sines, and RFC 4733 says that low-rate codecs cannot be guaranteed to reproduce tones accurately enough for automatic recognition. So a gateway detects the key and sends a small labeled packet instead: events 0 to 9 for the digits, 10 for star, 11 for hash and 12 to 15 for A to D. Cisco’s documentation files this under in-band methods, because the packet travels in the media stream beside the voice, and keeps out-of-band for digits sent through call signaling, such as SIP INFO. Often no tone crosses the wire at all.

What a recording cannot tell you

Decoding tones from a recording, which is what the tool on this page does, inherits these limits and adds some. If the call passed through a gateway that turned keys into event packets, there may be nothing to find. If the audio was squeezed by a low-rate codec, the tones may be distorted past recognition. Neither loss can be undone afterwards.

A telephone also protects its own signals in ways a recording does not. The 1960 design disabled the microphone while a key was down, so the caller’s voice could not sit on top of the tones. A recording of a room has no such switch, and speech louder than the keys will hide them. Echo does a different damage. An echo of one tone fills part of the pause before the next, and a receiver that waits for a clear gap may not find one. A speakerphone in a hard room does exactly that, and two presses of the same key blur into one.

Try the method on a clean case first. Choose the keypad source above and press 5. The page plays 770 Hz and 1336 Hz together for 160 ms, the two matching bars rise on the meter, and the readout shows 5. Press 5 twice and it shows 55, but only because the generator leaves at least 60 ms of silence between tones. This decoder needs about 30 ms of quiet before it will call a second press. It accepts a level difference of up to about 10 dB, wider than the standard’s 6 because a loudspeaker and a microphone add their own tilt, and it wants roughly 35 ms of steady tone before it believes anything.

It is worth saying plainly what the method cannot do. It cannot recover digits that were never sent as sound. It cannot pull tones out from under louder speech or music, and two sustained musical notes that fall close to a tone pair will read as a key. It reports what was pressed, never who pressed it or where the call went. A key held for three seconds is one digit, not thirty.

What remains impressive is how little was left to chance: eight frequencies a throat seldom produces two at a time, and receivers patient enough to wait 40 ms. Six decades on, the chord says one thing. Someone pressed a key.