The alignment problem of audio

Listening to different audio tracks often perceive different levels of volume. These continuous changes in volume between tracks and the next can be very annoying, can cause us to lose focus and constringerci constantly changing the volume level manually.
People in all those cases where you need to concatenate audio / video (Simple Media Player, TV, etc ...)

What to do?

We aim to balance the volume level between different sound sources.

The first problem is to find a function that describes the best possible sound pressure level of a sound.
The sound pressure level ( $L_p$ ) Is the logarithmic measure of the sound pressure with respect to a reference value: $L_p = 10\log_{10}(p/p_0)^2$
The sound pressure is a parameter, expressed in Pa, which represents the change in pressure compared to a condition of peace.

We will use the function Root Mean Square (RMS) to find the sound pressure level of a stream, it is calculated in this way; given a inzieme $X = \{x_1, x_2, ..., x_n\}$ The RMS is:

$X_{rms} = \sqrt{\frac{1}{n} \sum_{i=1}^{n}{x_i^2}}$

As if we calculate on a continuous function $f$ range $t_0, t_1$ its $f_{rms}$ will be:

$f_{rms} = \sqrt{\frac{1}{t_1 - t_0}\int_{t_0}^{t_1}[f(x)]^2 dx}$

How much change the volume?

With the RMS we can calculate the average sound level of a whole stream so ottenedo $M_{s}$ . Both $v$ the amplification factor and $M_{rms}$ the average value of the volume dedio that we would like in output, then:

$M_{rms} \sim v M_s$

$v \sim \frac{M_{rms}}{M_s}$

The amplification factor will go from $0$ to $1$ to reduce the volume, $1$ to leave it unchanged, and more $1$ to amplify it.

Conclusions

If we have multiple audio streams with different volume levels we can align them bringing them all at the same average volume. To do what we must first analyze each input stream, calculate its $M_s$ , From that deduce the amplification factor $v$ and apply it to the track.

I wrote a small program in Python that does the job. It consists of a library that takes care of all the transformations of sound volume and a small executable to run the tests with audio files.

Examples

Let's see some examples of the output.

 $. / Testgain - help
 . / Testgain vesion 0.2

 Usage:. / Testgain [OPTINS] [MP3/OGG ​​FILE ...]
 This program is used for testing volumegain library.

 OPTIONS:
     -P - play: play the stream
     <n>-R - rms <n>: set the default and normalized rms
                          apply it to the stream
     -Q - quiet: quiet mode
     -V - verbose: more verbose
     -V - version: print version info and exit
     -H - help: display this help end exit

 Report bugs to <danilo.abbasciano@gmail.com>

 $. / Testgain audio-v \ example/1.ogg
 Audio File: Audio example/1.ogg
 Type: ogg
 Channel: 0 Mean RMS: 0.198368826507 Pa
                 Mean RMS: -14.0505315166 dB
 Channel: 1 Mean RMS: 0.229194515258 Pa
                 Mean RMS: -12.7959155894 dB
 Mean:
 All Mean channel RMS: 0.213781670882 Pa

 $. / Audio testgain \ example / [1-3]. Ogg-r 00:12
 Audio File: Audio example/1.ogg
 All Mean channel RMS: 0.213781662184 Pa

 Audio File: Audio example/2.ogg
 All channel RMS Mean: 0.0407199536201 Pa

 Audio File: Audio example/3.ogg
 All Mean channel RMS: 0.206117526775 Pa

 - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~
 Changing volume.  File: Audio example/1.ogg
 All Mean channel RMS: 0.119991210077 Pa

 - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~
 Changing volume.  File: Audio example/2.ogg
 All Mean channel RMS: 0.119997166635 Pa

 - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~ - ~
 Changing volume.  File: Audio example/3.ogg
 All Mean channel RMS: 0.119992128875 Pa

Downloads

If you want more information download the PDF presentation (in English) here:
[Download file = 'volumegain-Summercamp-presentation.pdf' name = 'volumegain presentation']

If you want to program, including libraries, and examples testgain download this archive:
[Download file = 'volumegain-0.2.tgz' name = 'volumegain-0.2.tgz' version = '0 .2 ']