Representing sound

What you need to know

• ✓Sound is an analogue signal that must be converted to digital binary data using an Analogue-to-Digital Converter (ADC).
• ✓Sampling rate is the number of samples taken in a second, measured in hertz (one hertz is one sample per second).
• ✓Sample resolution (bit depth) is the number of bits allocated to each sample, giving 2ⁿ discrete quantisation levels.
• ✓Quantisation error is the difference between the continuous analogue wave amplitude and the nearest discrete digital level.
• ✓Sound file size formula: File size (in bits) = sampling rate (Hz) × sample resolution (bits) × duration (seconds).
• ✓To convert bits to bytes, divide by 8; to convert bytes to kilobytes (kB), divide by 1,000, and by 1,000 again for megabytes (MB).

What you don’t need

• Lossy vs lossless audio compression codecs like MP3 or FLAC (covered in 3.3.8).
• Fourier transforms and spectral frequency analysis.
• Complex MIDI file formats and synthesizer protocols.

Worked examples

1. Calculate the size in MB of a 2-minute recording sampled at 44,100 Hz with a 16-bit sample resolution.

   1. Convert duration to seconds: 2 minutes × 60 = 120 seconds.
   2. Calculate total bits: 44,100 × 16 × 120 = 84,672,000 bits.
   3. Convert to bytes by dividing by 8: 84,672,000 ÷ 8 = 10,584,000 bytes.
   4. Convert to kB, then MB: 10,584,000 ÷ 1,000 = 10,584 kB; 10,584 ÷ 1,000 = 10.584 MB.

   Answer: 10.584 MB

2. A voice recording lasts 30 seconds, sampled at 8,000 Hz with an 8-bit sample resolution. Calculate its size in kB.

   1. Calculate total bits: 8,000 × 8 × 30 = 1,920,000 bits.
   2. Convert to bytes: 1,920,000 ÷ 8 = 240,000 bytes.
   3. Convert to kB: 240,000 ÷ 1,000 = 240 kB.

   Answer: 240 kB

3. Explain what is meant by quantisation error, and describe how it can be reduced.

   1. State definition: Quantisation error is the difference between the actual continuous analogue wave amplitude and the nearest discrete quantisation level assigned by the ADC.
   2. State remedy: It can be reduced by increasing the sample resolution (bit depth), which creates more quantisation levels with smaller gaps.

   Answer: Quantisation error is the difference between the continuous analogue wave amplitude and the nearest discrete digital level allocated by the ADC. It is reduced by increasing the sample resolution (bit depth).

Common mistakes

• ✕Forgetting to convert duration from minutes to seconds before multiplying.
• ✕Leaving the answer in bits when the question asks for bytes, or dividing by 1,024 instead of 1,000 for kB and MB.
• ✕Confusing sampling rate (horizontal time frequency) with sample resolution (vertical amplitude levels).