Sampling is the process of measuring the value of an analog signal at regular intervals to convert it into a digital signal. It is the first step in sound digitization, used by all digital devices, including smartphones.
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How to measure it in class
With the FizziQ app, you can explore the effects of sampling on sound quality.
Steps:
- Open FizziQ and observe that the microphone samples sound at 44100 Hz (audio standard)
- Use the synthesizer to generate sounds of different frequencies
- Observe that beyond 22000 Hz, sounds are no longer captured correctly (Nyquist limit)
- Compare the recording of a high-pitched sound (close to the limit) with a low-pitched sound
- Analyze possible artifacts at high frequencies with the spectrogram
Scientific activities on this topic
Possible extensions with FizziQ: understanding the limitations of the smartphone microphone, studying aliasing (spectral folding) with high-pitched sounds, and comparing different recording qualities.
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The sampling process:
An analog sound signal varies continuously over time. To digitize it, its amplitude is measured at regular instants, spaced T seconds apart (sampling period). The sampling frequency fₑ = 1/T indicates how many measurements are taken per second.
Common sampling frequencies:
| Application | Frequency (Hz) |
|---|---|
| Telephone | 8,000 |
| Low-quality multimedia | 22,050 |
| Audio CD | 44,100 |
| DVD/Blu-ray | 48,000 |
| Pro studio | 96,000 - 192,000 |
The Shannon-Nyquist theorem:
To faithfully reconstruct a signal, the sampling frequency must be at least twice the maximum frequency of the signal. This is why the CD (44100 Hz) can reproduce sounds up to 22050 Hz, slightly above the human audible limit.
Aliasing:
If a sound exceeds the Nyquist frequency, it is “folded” back to lower frequencies, creating audible artifacts. Audio systems use anti-aliasing filters to avoid this problem.
Formula
Nyquist frequency: f_Nyquist = fₑ / 2
Shannon theorem: fₑ ≥ 2 × f_max
where:
- fₑ: sampling frequency (Hz)
- f_max: maximum frequency of the signal to be digitized
- f_Nyquist: maximum frequency reproducible without distortion
Application examples
- A smartphone samples at 44100 Hz, allowing it to capture sounds up to 22 kHz
- Telephone voice, sampled at 8000 Hz, does not transmit high harmonics (“metallic” sound)
- Professional studios use 96 kHz or more for a safety margin during processing
- A 128 kbps MP3 file samples at 44100 Hz but compresses the data
FAQ
Q: Why does the CD use exactly 44100 Hz? A: It is a historical compromise related to video tape recording techniques of the 1970s-80s. It is slightly above the theoretical minimum (40000 Hz for 20 kHz).
Q: Does a higher sampling rate give better sound? A: Beyond 48 kHz, the improvement is imperceptible to the human ear. High sampling frequencies (96, 192 kHz) are mainly useful for professional audio processing.
Q: What is FizziQ’s sampling frequency? A: FizziQ uses 44100 Hz, the CD standard, which allows analysis of all audible sounds.
Related concepts
Nyquist Frequency