51 lines
1.9 KiB
Markdown
51 lines
1.9 KiB
Markdown
|
---
|
||
|
|
tags: [sound, binary, analogue]
|
||
|
|
created: Friday, December 27, 2024
|
||
|
|
---
|
||
|
|
|
||
|
|
# Binary encoding of sound
|
||
|
|
|
||
|
|
Sound is a change in air pressure.
|
||
|
|
|
||
|
|
To record sound, we convert the change in air pressure into an electrical signal
|
||
|
|
by means of a microphone. Effectively, the same natural waveform is converted
|
||
|
|
from one medium (the vibration of air molecules) into another medium (electrical
|
||
|
|
charge in a field) whilst retaining the same morphology. See
|
||
|
|
[Recording and processing sound]().
|
||
|
|
|
||
|
|
The resulting electrical signal is analogue: it has a continuous and variable
|
||
|
|
frequency and amplitude and thus can have any value at any given moment.
|
||
|
|
|
||
|
|
To encode this information digitally we need to make the continuous analogue
|
||
|
|
single discrete, so that it can represented with a finite set of symbols (bits).
|
||
|
|
|
||
|
|
This process is known as **quantization** and consists in sampling the analogue
|
||
|
|
waveform. This means taking a measurement of it at different points in time -
|
||
|
|
each second.
|
||
|
|
|
||
|
|
CDs sample the audio source at a rate of 44.1 kHz: 44, 100 measurements of the
|
||
|
|
signal per second.
|
||
|
|
|
||
|
|
The measurements are then stored in a digital format: bits. The amount of bits
|
||
|
|
used to record the measurement is the **bit-depth**. Each measurement is rounded
|
||
|
|
to the nearest available digital value. CDs have a depth of 16 bits. Thus each
|
||
|
|
measurement can be one of $16^2 = 65,536$ possible values.
|
||
|
|
|
||
|
|
With sampling at a given bit-depth established, the **bitrate** can be derived.
|
||
|
|
|
||
|
|
This is the sampling rate (number of measurements per second) divided by the
|
||
|
|
number of bits per sample (bit-depth), multiplied by the number of channels.
|
||
|
|
|
||
|
|
Thus for stereo CDs this is:
|
||
|
|
|
||
|
|
$$
|
||
|
|
(44100 / 16 ) \middot 2 = 1411200
|
||
|
|
$$
|
||
|
|
|
||
|
|
Or 1.4 Mb/s
|
||
|
|
|
||
|
|
> Even with a high bitrate (as with CDs) the process still necessarily involves
|
||
|
|
> a loss of information when converting sound from analogue to digital. However,
|
||
|
|
> given a high enough value for the sampling rate and bit-depth, the differences
|
||
|
|
> are imperceptible to the human ear.
|