## Let’s talk about touch-tone telephones!

Posted 8/16/16

You remember the soft beeping of old phones when you punched in numbers? I wonder how those work! Sounds like a good premise for a project. Let’s write a script that takes a bunch of numbers and outputs the appropriate tones, and no cheating by saving off recordings of the beeps.

### Signal Overview

Dual Tone Multiple Frequency signals are a way of transmitting computer-readable data over analog lines. It works by combining two different sine waves to create a single tone:

1209 Hz 1336 Hz 1477 Hz 1633 Hz
697 Hz 1 2 3 A
770 Hz 4 5 6 B
852 Hz 7 8 9 C
941 Hz * 0 # D

Why does it work this way? Ruggedization. Analog audio equipment can have weird distortions and pitch shifts, and if we used a single sine wave for each digit then those distortions could lead to misinterpreting a signal. Very awkward if you dial a phone number and it connects to the wrong person. By creating a dual-tone signal each digit is extremely distinct from one another and are almost impossible to confuse.

What are those “ABCD” digits? My phone doesn’t have them!

Those are used within the telephone company for some internal controls. They’re interesting, and you can read more about them here, but they’re outside the scope of my project.

### Trigonometry

If you’re like me and you forgot your trigonometry, don’t worry! Adding two waves is very simple. Sine waves output between -1 and 1. A higher frequency means the wave repeats itself more quickly, while a higher wavelength (and lower frequency) means the waves are more drawn out.

We can add two waves by layering them over each other on a graph, and adding their points together. If one wave is at -1, and the other is at 0.25, then the new wave has a point of -0.75. The effect looks like this:

### The Code

At this point all we have left is implementation. I went at this in a clunky way:

• Figure out how long our tone needs to be

• Choose the two waves we need to make up a digit

• Create an array of outputs, where each entry is the noise of the digit at a specific point

• Convert the array of outputs to a wave file

The code is fairly simple, and all up on GitHub. The core is calculating the value of a wave at a certain point in its period:

```Math::sin(position_in_period * TWO_PI) * max_amplitude
```

The amplitude (height of the wave) determines the volume of the tone.

After that, all that’s left is using the Ruby Wavefile Gem to encode the array of samples as noise and save it to disk, and then a little glue code to parse user input and trigger all the calculations.

One day this might have been an awesome tool for Phone Phreaking, but today most of the telephone network is digital, and there’s only so much you can do with a tone generator. So it goes.