Digital representation of sound

Overview

Recall questions on sampling rate and sample resolution, the Nyquist theorem and the CD sampling rate, and calculating the size of a sound file.

What you need to know

Answer each one before you reveal it.

Questions from this subtopic

Each one with the model answer underneath.

1. 1

   Describe how a sound is represented digitally.

   Model answer

   Sound is a continuously varying pressure wave, which a microphone turns into a continuously varying voltage. That analogue signal is sampled at regular intervals: at each interval the amplitude is measured and rounded to the nearest of the levels available, and the result is stored as a binary number. The sound file is therefore a long sequence of sample values, and playing it back means feeding those values to a digital to analogue converter.

2. 2

   What is sample resolution, and what effect does it have?

   Model answer

   Sample resolution is the number of bits used to store each individual sample, so it fixes how many amplitude levels are available — n bits give 2ⁿ levels. A higher resolution means the levels are more finely spaced, so each measurement is rounded less and the recording reproduces the original amplitudes more accurately, at the cost of proportionally more storage.

3. 3

   What is the sampling rate, and what effect does it have?

   Model answer

   The sampling rate is the number of samples taken per second, measured in hertz. A higher rate captures the shape of the waveform more often, so rapid changes and higher frequencies are reproduced faithfully, giving better quality — again at the cost of proportionally more storage.

4. 4

   State the Nyquist theorem.

   Model answer

   To reconstruct a signal accurately, the sampling rate must be at least twice the highest frequency present in that signal. Sampling any slower loses information that cannot be recovered.

5. 5

   Apply the Nyquist theorem to explain the sampling rate used for audio CDs.

   Model answer

   Human hearing extends to roughly 20 kHz, so the highest frequency to be captured is about 20 000 Hz. Nyquist requires at least twice that, which is 40 000 samples per second. The CD rate of 44 100 Hz is a little above that minimum, leaving margin for the filters used to remove frequencies above the audible range.

6. 6

   What happens if a signal is sampled below the Nyquist rate?

   Model answer

   Aliasing occurs. Frequencies above half the sampling rate are not simply lost — the samples taken from them fit a lower frequency just as well, so they are reconstructed as spurious lower-frequency tones that were never in the original. The result is audible distortion, and it cannot be corrected afterwards because the samples are genuinely ambiguous.

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