# What's the frequency?

##### Class practical

The demonstration models the process of sampling an analogue signal at regular intervals in order to encode information digitally.

Students become familiar with the phenomenon of aliasing. They learn that the sampling frequency must be at least twice the highest frequency contained in a signal.

#### Apparatus and materials

OHP acetate or tracing paper, clean sheets

OHP pen

#### Health & Safety and Technical notes

The frequency cards may be printed onto OHP acetate sheets.

The sample cards should be printed on card or thick paper and then narrow slots cut out as indicated.

#### Procedure

a Place sampler card 1 over frequency card C, then place a sheet of clean acetate or tracing paper on top of the sampler card.

b Make crosses or large dots at all the places where the wave is visible through the sampler card.

c Remove the sampler and frequency cards and join the dots with a simple wavy line.

d Reveal card 1 and compare it with the reconstructed wave. The two have the same repeat distance and similar amplitude.

e Now repeat the procedure with sampler card 4 and frequency card A, being careful not to reveal card 4 to the observer until after you have carried out the sampling and reconstruction. This time, the reconstructed wave is far from a faithful reproduction of the original - the repeat distance is much greater - which is a surprising result.

f Repeat with other combinations of sampler and frequency cards.

#### Technical notes

1 This works well as a demonstration to the whole class using an OHP. Alternatively, students could perform the demonstration themselves in small groups - but the element of surprise is then absent.

2 The frequency cards model a signal which varies sinusoidally with time.

Provided a signal is sampled at regular intervals with a sampling frequency at least twice the signal frequency, then the original signal frequency can be faithfully reconstructed. If the sampling frequency is less than twice the signal frequency, the reconstructed signal is not faithful to the original as it has a different frequency. The introduction of spurious frequencies into a signal, as a result of inappropriate sampling, is known as aliasing.

In telecommunications, care must be taken to ensure that the sampling frequency is at least twice the highest frequency contained in a signal.

This experiment comes from Salters Horners Advanced Physics©, University of York Science Education Group.

Diagrams are reproduced by permission of the copyright holders, Heinemann.

This experiment was safety-checked in December 2004