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Measurements

Sampling Frequency (or Sampling Rate)

When a voltage is applied to a digital voltmeter, a variable voltage source inside the meter is increased from zero until it reaches the same value as the applied voltage. The display then indicates the value of the internal voltage source. This process of comparing the external voltage with an internal voltage is called sampling the external voltage and, of course, takes a certain time. Suppose the sampling process occurs 4 times a second. Any change in voltage which lasts for less than ¼ of a second will (probably) be missed. For this reason, a digital instrument should operate with a sampling frequency much higher than the expected frequency of variation of the quantity being measured. (The speed of response of an analogue meter is also limited. In the case of the analogue meter the limit is due to the inertia of the moving parts.)

The importance of having a (relatively) high sampling rate can be seen if we consider the process of digital sound recording. A varying voltage from, for example, a microphone must be converted into a series of numbers representing the magnitude of the voltage at regular intervals. In other words, what we need is a fast response digital voltmeter. (The device used is actually called an analogue to digital converter.) These numbers are then recorded and when "replayed" can be used to reproduce the original sound.

The first two diagrams below represent the voltage to be recorded (left) and its digital equivalent (right) produced using a sampling frequency which is much higher than the frequency of the original sound.

The marks on the horizontal axis represent the instants at which the sampling occurred.

At this sampling frequency the original wave is recognisable and could be reproduced accurately with the aid of filters.

Now consider using a sampling rate which is lower than the frequency of the sound to be recorded. This situation is represented by the diagrams below.

In this case it would be impossible to extract the original sound. It has been shown (by C. Shannon in 1948) that, to be able to obtain a good "copy" of the original sound, the sampling frequency must be at least twice as high as the highest frequency of sound to be recorded.

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