Author:

• Name: Edward Giles
  Location: AU - Commonwealth of Australia (Australia)

To build:

    make

Bugs and (Mis)features:

The current status of this entry is:

STATUS: INABIAF - please DO NOT fix

For more detailed information see 2020/giles in bugs.html.

To use:

    ./prog < dtmf.wav

    ./prog [digits] > digits.wav

where dtmf.wav is a WAV file of the dialling of a number being dialled with DTMF (Dual-tone multi frequency) (more commonly known as Touch-Tone) and [digits] is a sequence of digits that will be converted to the DTMF sound!

Try:

    ./try.sh
    ./prog < pi.wav

    # See
    ./prog 867-5309 > jenny.wav

If the script try.sh did not play a WAV file, it means you do not have SoX installed; see the FAQ on “using entries that require sound”. In this case install it and try it again or play the files jenny.wav and ioccc28.wav in a program that can play WAV files.

NOTE: the phone number of jenny.wav comes from https://en.wikipedia.org/wiki/867-5309/Jenny.

Judges’ remarks:

A cross platform utility for both encoding and decoding touch tones.

Author’s remarks:

Introduction and Usage

This program encodes and decodes dual-tone multiple frequency signals used in telephone systems, more commonly known as Touch-Tones.

If the program is executed with no arguments, it will read a WAV file from standard input, decode the touch-tones in the file, and output the corresponding digits to standard output. This program only supports WAV files that have exactly 16 bits per sample, but it allows any sample rate and any number of audio channels.

    $ ./prog < pi.wav
    31415926

If the program is executed with a command-line argument, it will generate the tones corresponding to the specified characters, writing them to standard output as a WAV file.

    $ ./prog 867-5309 | aplay

Interesting Features

• When compiled with gcc -pedantic -Wall -Wextra there are no compiler warnings.
• This program can be successfully compiled and run on Windows, using both Microsoft’s C compiler and TCC.
• This program resamples the incoming audio, so that it can accept audio data at any sample rate.
• The code that generates the output sine-waves is the same as the code that looks for sine-waves in the input. (see Algorithm Details for roughly how this works).
• Despite handling lots of sine waves, the program only uses basic arithmetic operations. It does not depend on libm.
• All type punning is done with memcpy(3) so there are no strict-aliasing violations.
• The size of the source code using the IOCCC size tool is 1963, the year the first push-button telephones were made available to customers.
• The source code (not counting the C pre-processor) is roughly in the shape of a telephone handset.

Assumptions

• Code is compiled using the C99 or C11 standard.
• CHAR_BIT == 8.
• Machine is little-endian.
• int16_t, uint16_t, and uint32_t exist.
• int16_t is 2’s-complement.
• double is an IEEE 754 binary64 floating-point type.
• sizeof(double) == 8.

Obfuscations

• DSP code is inherently somewhat difficult to understand.
• Lots of identifier reuse. Each identifier is used for about 2.2 different tasks, on average. For example, aa is both a variable and a macro for error handling, and memcpy(3) is both a library function and a oto label.
• Most of the identifiers are only 1 or 2 characters long, and are unrelated to their actual function.
• The f macro is used to unroll some of the loops.
• Some numerical constants are replaced with character literals, so the actual value is unclear.
• All of the strings used by the program have been combined into a single string literal.
• Most of the values used for the actual signal-processing all reside in one array, named l. This array is usually accessed at index z plus a constant. Accesses of this type have been rewritten from, e.g. l[z+17] to 17[l+z]. [l+z] ends up occurring quite often, so I created the macro a as a shorthand.

Algorithm Details

Each tone in a DTMF signal is a combination of two frequencies. The lower frequency determines which row the digit is in, and the higher frequency determines the column. There are 4 possible row frequencies and 4 possible column frequencies.

    |            | **1209 Hz** | **1336 Hz** | **1477 Hz** | **1633 Hz** |
    |------------|-------------|-------------|-------------|-------------|
    | **697 Hz** | 1           | 2 abc       | 3 def       | A           |
    | **770 Hz** | 4 ghi       | 5 jkl       | 6 mno       | B           |
    | **852 Hz** | 7 pqrs      | 8 tuv       | 9 wxyz      | C           |
    | **941 Hz** | *           | 0           | #           | D           |

This program determines which frequencies are present in the input by passing it through a set of 8 virtual resonators, each tuned to one of the frequencies used for DTMF. These can be implemented using only basic arithmetic, and they are able to ‘select’ a specific frequency from the input sound, blocking all other frequencies from reaching the output. The loudness of the sound output from each resonator can therefore be used as a measure of how much of a particular frequency was present in the input. The program then decides, over the course of one tone, which row frequency and which column frequency were most prominent.

Tones are generated using those same resonators by providing an impulse as input. An impulse can be thought of as consisting of sine-waves at all frequencies, and when it is put through one of the resonators, the result is a single pure sine wave.

Primary files

• prog.c - entry source code
• Makefile - entry Makefile
• prog.orig.c - original source code
• try.sh - script to try entry
• pi.wav - WAV file of touch tone for leading decimal digits of pi

Secondary files

• 2020_giles.tar.bz2 - download entry tarball
• README.md - markdown source for this web page
• dtmf.bin - dual-tone multi frequency / touch-tone wav file
• .entry.json - entry summary and manifest in JSON
• .gitignore - list of files that should not be committed under git
• .path - directory path from top level directory
• index.html - this web page

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