Sound Representation
Analogue to Digital
Sound is an analogue signal, a continuous wave of air pressure. To store sound digitally, it must be converted into binary using analogue-to-digital conversion (ADC).
Analogue Sound Wave: ~~~~∿∿~~~~∿∿~~~~
(continuous)
Digital Samples: | | | | |
7 3 9 2 ...
(discrete measurements)
Key Terms
Sample Rate
- The number of measurements (samples) taken per second
- Measured in Hertz (Hz)
- Higher sample rate → more accurate representation → larger file size
- Example: CD quality = 44,100 Hz (44,100 samples per second)
Bit Depth (Sample Resolution)
- The number of bits used to store each sample
- Determines the precision of each measurement
- Higher bit depth → closer to original analogue sound → larger file size
- Example: CD quality = 16 bits per sample (2¹⁶ = 65,536 possible values = 96 dB range)
- DVD/Blu-ray quality = 24 bits per sample (2²⁴ = ~16.7 million values = 144 dB range)
Sample Interval
- The time between each sample = 1 ÷ sample rate
- Opposite of sample rate, not what we calculate with directly
Bandwidth
- The total range of values storable per sample = 2^(bit depth)
- Higher bit depth → wider bandwidth → more dynamic range
Amplitude
- The height of the sound wave at any point
- Corresponds to the loudness of the sound
File Size Formula
File size (bits) = sample rate × bit depth × duration (seconds)
Example: Sample rate = 44,100 Hz, bit depth = 16 bits, duration = 30 seconds
= 44,100 × 16 × 30
= 21,168,000 bits
= 21,168,000 ÷ 8 = 2,646,000 bytes
= 2,646,000 ÷ 1024 ≈ 2,584 KiB ≈ 2.52 MiB
Effect of Increasing Sample Rate or Bit Depth
| Change | Quality | File Size |
|---|---|---|
| ↑ Sample rate | Higher (more accurate waveform) | Larger |
| ↓ Sample rate | Lower | Smaller |
| ↑ Bit depth | Higher (more precise samples) | Larger |
| ↓ Bit depth | Lower | Smaller |
Quality Comparison
| Medium | Sample Rate | Bit Depth | File Size |
|---|---|---|---|
| CD | 44,100 Hz | 16-bit | Moderate |
| DVD/Blu-ray | 96,000+ Hz | 24-bit | Large |
| Compressed (MP3) | 44,100 Hz | ~128kbps (lossy) | Small |
Exam Questions
Q: What is sample rate and how does it affect quality?
Sample rate is the number of times per second the analogue sound is measured. A higher sample rate captures more detail, producing a higher quality recording but a larger file.
Q: What is bit depth?
The number of bits used to store each sample. A higher bit depth gives more precise measurements, closer to the original sound, but increases file size.
Q: Calculate the file size of a 3-second recording at 6 Hz sample rate and 4-bit depth.
6 × 4 × 3 = 72 bits = 9 bytes.
Exam Tip
Distinguish carefully: sample rate = how often you measure (per second); bit depth = how precisely you measure each time. Both affect quality AND file size in the same way.