The app controls are labelled in Italian: below, each label is given as it appears in the app, followed by its English meaning.

Analogue sound and digital sound

1. Click here to start the app, choose the "seno" (sine) wave, switch the sound on, and repeatedly use the "ricampiona" (resample) button.
   • This button changes the number of segments into which the function is divided in time. At the start there are 1024. At the first click they become 32, then they are halved at each further click.
   • Observe how the spectrum changes: spurious frequencies appear. At the first click harmonics 31 and 33 appear, at the second also 15 and 17, then 7 and 9, and so on. That is, the first harmonic to the right and to the left of the sampling frequency always appears. (For a more detailed description see the page on the spectrum of radio signals.)
   • You can therefore see that digital sampling of sound (that is, representing sound over discrete time intervals rather than continuously) introduces spurious harmonics.
2. You can now increase the number of harmonics using the bar on the right, to see that the phenomenon affects the whole spectrum.
3. Now select the "triangolo" (triangle) wave, and repeatedly use the "quantizza" (quantise) button.
   • Quantisation is the process by which a continuous function is approximated by a discrete set of values. It is the process on which the digitisation of any signal (not only audio) is based. At the first click the signal is quantised on 32 values, then the number is halved at each click. Since ${\displaystyle 32=2^5}$, ${\displaystyle 16=2^4}$, etc., the first quantisation is said to correspond to 5-bit audio, the second to 4-bit, and so on. The quantisations common in good-quality audio files are usually 16 or 24 bit.
   • So quantisation also produces spurious harmonics, that is, artefacts in the signal. This is very important when trying to compress a file (that is, to reduce its number of bits). Good compression is obtained only when these artefacts cannot be perceived (see critical bands and masking).