2025-01-01 15:57:56 +00:00
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---
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tags: [sound, binary, analogue]
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created: Friday, December 27, 2024
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---
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# Binary encoding of sound
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Sound is a change in air pressure.
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To record sound, we convert the change in air pressure into an electrical signal
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by means of a microphone. Effectively, the same natural waveform is converted
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from one medium (the vibration of air molecules) into another medium (electrical
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charge in a field) whilst retaining the same morphology. See
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2025-01-02 17:31:19 +00:00
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[Recording and playback of sound](Recording_and_playback_of_sound.md).
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2025-01-01 15:57:56 +00:00
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The resulting electrical signal is analogue: it has a continuous and variable
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frequency and amplitude and thus can have any value at any given moment.
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To encode this information digitally we need to make the continuous analogue
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single discrete, so that it can represented with a finite set of symbols (bits).
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This process is known as **quantization** and consists in sampling the analogue
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waveform. This means taking a measurement of it at different points in time -
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each second.
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CDs sample the audio source at a rate of 44.1 kHz: 44, 100 measurements of the
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signal per second.
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The measurements are then stored in a digital format: bits. The amount of bits
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used to record the measurement is the **bit-depth**. Each measurement is rounded
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to the nearest available digital value. CDs have a depth of 16 bits. Thus each
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measurement can be one of $16^2 = 65,536$ possible values.
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2025-01-02 17:31:19 +00:00
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With sampling at a given bit-depth established, the **bit-rate** can be derived.
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2025-01-01 15:57:56 +00:00
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This is the sampling rate (number of measurements per second) divided by the
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number of bits per sample (bit-depth), multiplied by the number of channels.
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Thus for stereo CDs this is:
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$$
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2025-01-01 16:02:50 +00:00
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(44100 / 16 ) \cdot 2 = 1411200
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2025-01-01 15:57:56 +00:00
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$$
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Or 1.4 Mb/s
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2025-01-02 17:31:19 +00:00
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> Even with a high bit-rate (as with CDs) the process still necessarily involves
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2025-01-01 15:57:56 +00:00
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> a loss of information when converting sound from analogue to digital. However,
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> given a high enough value for the sampling rate and bit-depth, the differences
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> are imperceptible to the human ear.
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