Sound Representation

This lesson covers how computers represent digital audio, including sampling, sample rate, bit depth, file size calculations, the Nyquist theorem, and the comparison between MIDI and digital audio. This is required for the OCR H446 specification.

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Analogue vs Digital Sound

Sound is a continuous (analogue) wave of air pressure changes. Computers store data digitally (as discrete binary values), so analogue sound must be converted to digital form.

Aspect	Analogue	Digital
Signal	Continuous	Discrete (sampled)
Quality	Perfect representation	Approximation
Storage	Physical medium (vinyl, tape)	Binary data
Copying	Degrades with each copy	Perfect copies

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Sampling (Analogue-to-Digital Conversion)

Sampling is the process of measuring the amplitude (volume level) of an analogue sound wave at regular time intervals and recording each measurement as a binary number.

How Sampling Works

1. The analogue sound wave enters a microphone, which converts it to an electrical signal.
2. An ADC (Analogue-to-Digital Converter) measures the signal's amplitude at regular intervals.
3. Each measurement (sample) is stored as a binary number.
4. The sequence of samples forms the digital representation of the sound.

Key Parameters

Parameter	Definition	Effect
Sample rate	The number of samples taken per second (measured in Hertz, Hz)	Higher = more accurate representation
Bit depth	The number of bits used to store each sample	Higher = more precise amplitude values
Duration	The length of the audio in seconds	Longer = larger file

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Sample Rate

The sample rate determines how often the analogue signal is measured per second.

Sample Rate	Quality	Use Case
8,000 Hz (8 kHz)	Telephone quality	Voice calls
22,050 Hz (22.05 kHz)	AM radio quality	Low-quality audio
44,100 Hz (44.1 kHz)	CD quality	Music CDs
48,000 Hz (48 kHz)	DVD/broadcast quality	Video production
96,000 Hz (96 kHz)	Studio quality	Professional recording

A higher sample rate captures more detail of the original waveform, producing a more accurate digital representation.

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The Nyquist Theorem

The Nyquist theorem (also called the Nyquist-Shannon sampling theorem) states:

The sample rate must be at least twice the highest frequency in the original sound to accurately reproduce it.

Minimum sample rate = 2 x highest frequency

Why 44,100 Hz for CDs?

Human hearing ranges from approximately 20 Hz to 20,000 Hz (20 kHz). By the Nyquist theorem:

Minimum sample rate = 2 x 20,000 = 40,000 Hz

CD quality uses 44,100 Hz, which slightly exceeds the Nyquist minimum, providing a safety margin.

What Happens Below the Nyquist Rate?

If the sample rate is less than twice the highest frequency, aliasing occurs — false low-frequency signals appear in the digital audio that were not present in the original sound. This causes distortion.

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Bit Depth

Bit depth (also called sample resolution) determines the number of possible amplitude levels for each sample.

Bit Depth	Amplitude Levels	Quality
8 bits	2^8 = 256	Low quality, noisy
16 bits	2^16 = 65,536	CD quality
24 bits	2^24 = 16,777,216	Studio quality
32 bits	2^32 = ~4.3 billion	Professional mastering

Effect of Bit Depth

• Higher bit depth = more amplitude levels = smoother representation of the wave = better quality.
• Lower bit depth = fewer amplitude levels = the wave is approximated more coarsely = quantisation noise (a hissing/buzzing artefact).