Learning Objectives
- Explain why analogue sound must be sampled before a computer can process it.
- Describe the roles of a microphone and analogue-to-digital conversion.
- Define sample rate and sample resolution.
- Explain how sample rate and sample resolution affect accuracy and file size.
- Apply sound representation concepts to recording scenarios.
Key Terms
- Analogue sound wave
- A continuously changing representation of sound amplitude over time.
- Sampling
- Measuring the amplitude of an analogue signal at regular time intervals.
- Sample rate
- The number of samples taken each second, measured in hertz.
- Sample resolution
- The number of bits used to store each sample value.
- Quantisation
- Assigning a measured amplitude to one of the available digital levels.
- Analogue-to-digital converter
- Hardware that converts sampled analogue measurements into binary values.
Why Sound Must Be Digitised
Sound travelling through air is a continuous wave of pressure changes. A computer cannot directly store a continuously varying physical wave. The sound must be converted into a sequence of numeric measurements, and those measurements must be represented in binary.
A microphone converts pressure changes into an analogue electrical signal. An analogue-to-digital converter measures the signal repeatedly. Each measurement becomes a sample. The sample value is rounded to one of the levels available at the chosen sample resolution and stored as a binary number.
The complete digital recording is therefore an ordered sequence of sample values. During playback, the values can be converted back into an approximate analogue signal and sent to a loudspeaker.
Sample Rate
Sample rate is the number of samples taken every second. It is measured in hertz, where one hertz means one sample per second. A rate of 44100 Hz means 44100 amplitude measurements are stored for each second of sound.
A higher sample rate records the wave at more time points. It can reproduce rapid changes more accurately and usually improves the faithfulness of the recording. It also creates more sample values, so file size and the amount of data transmitted increase in direct proportion to sample rate.
If sample rate is doubled while all other settings and duration remain the same, the number of samples and raw file size double.
Sample Resolution
Sample resolution is the number of bits used for each sample. More bits provide more possible amplitude levels because n bits provide 2^n patterns. This allows each measured amplitude to be rounded to a closer digital level.
A higher sample resolution reduces quantisation error and usually improves the accuracy and dynamic detail of the recording. It also increases the bits stored for every sample. Doubling the number of bits per sample doubles the raw data size when all other factors remain fixed.
Sample resolution changes vertical amplitude precision; sample rate changes how frequently the wave is measured over time. These are different characteristics and should not be confused.
Quality And File-Size Trade-Off
Increasing sample rate and sample resolution generally improves recording accuracy, but it also increases storage requirements, transmission time and required bandwidth. A system designer chooses settings appropriate to purpose.
A spoken-message system may accept lower settings because speech can remain understandable with less detail. Music production or archival recording may use higher settings because subtle changes matter. An examination answer should compare the specific factor named and state both the quality and file-size consequences.
Excessively low sample rate can fail to capture rapid changes in the wave. Low sample resolution provides too few amplitude levels, causing larger rounding differences between the original measurement and stored value.
From Recording To Playback
The recording path can be described as sound wave, microphone, analogue electrical signal, repeated sampling, quantisation into sample values, binary storage and processing. During playback, the stored values are read in order, converted into an analogue signal and used to drive a loudspeaker.
For syllabus questions, focus on sampling, sample rate, sample resolution, accuracy and file size. Detailed audio formats and specialist signal theory are not required.
Sample Rate And Sample Resolution
| Feature | Sample Rate | Sample Resolution |
|---|---|---|
| Definition | Samples taken per second | Bits used for each sample |
| Main accuracy effect | More or fewer measurements over time | More or fewer amplitude levels |
| If increased | Wave is measured more frequently | Each amplitude is represented more precisely |
| File-size effect | More sample values are stored | More bits are stored per sample |
| Unit | Hertz | Bits |
Digitising Sound Stages
| Stage | Purpose |
|---|---|
| Microphone | Converts air-pressure changes into an analogue electrical signal. |
| Sampling | Measures the signal at regular intervals. |
| Quantisation | Rounds each measurement to an available level. |
| Binary encoding | Represents the level using bits. |
| Storage or transmission | Keeps or sends the ordered sample values. |
Worked Examples
Effect Of Doubling Sample Rate
Question: A recording uses 22050 samples per second. The rate is changed to 44100 samples per second. What happens if all else is unchanged?
- Twice as many samples are taken in each second.
- The wave is measured more frequently.
- The raw file size doubles.
Answer: Accuracy is likely to improve and raw file size doubles.
Possible Sample Levels
Question: How many amplitude levels are available with 12-bit sample resolution?
- Use 2^12.
Answer: 4096 levels.
Comparing Two Recordings
Question: Recording A uses 8-bit samples and Recording B uses 16-bit samples at the same sample rate and duration. Compare them.
- B has 2^16 possible codes per sample, while A has 2^8.
- B can represent amplitude more precisely.
- B stores twice as many bits per sample.
Answer: B is likely to be more accurate but has twice the raw file size.
Examination Guidance
- Define sample rate as samples per second, not bits per second.
- Define sample resolution as bits per sample, not the number of samples.
- When a setting increases, state both the quality effect and the file-size effect.
- Use the word analogue for the original continuously varying sound signal.
Common Mistakes
- Saying the microphone directly creates binary values; conversion hardware is needed.
- Claiming higher sample rate gives more possible amplitude values; that is sample resolution.
- Claiming higher sample resolution takes samples more often; that is sample rate.
- Saying a higher-quality recording is smaller because it is clearer.
Knowledge Check
1. What is sampling?
2. What does 48000 Hz mean?
3. Why does higher sample resolution usually improve accuracy?
4. What happens to raw file size if sample resolution changes from 8 bits to 24 bits?
5. Which device initially converts sound pressure to an electrical signal?
