# 6.4 - 6.4 Properties of Discrete Signals Elementary but...

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94 6.4 Properties of Discrete Signals Elementary, but important and special properties of discrete signals that represent real numbers Accuracy The accuracy of the approximation of a discretised signal will depend on both the sampling interval ( time resolution ), and on the amplitude resolution of the analog-to-digital converter (ADC). Amplitude resolution Suppose the ADCs can operate over some limited voltage range, Δ S = +/- 5V. The resolution is related to the smallest possible change in voltage that can be represented by the binary number system, and so can be expressed as Δ S / 2 n . +5V -5V 0 Δ S 2 numbers for n bit word. Resolution in V, δ S = Δ S/2 e.g. = 10/4096 = 2.44 mV It is fixed , in V n n For example, if the ADC’s have a resolution of 12 bits (as is frequently the case) to cover Δ S , then the resolution in volts, δ S , is δ S = 10 / 2 12 = 10/4096 = 2.44 x 10 -3 V. Expressed as a fraction of the input range we can write δ S / Δ S = ( Δ S /2 n )/ Δ S = 2.4 x 10 -4 = 0.024%. If an input signal, s , fluctuates from -0.5 to +0.5 V, then the resolution expressed as a fraction of the input signal range, ( Δ S /2 n )/ Δ s , is 2.44 x 10 -3 , or 0.24%. This is still quite acceptable and gives some room to avoid saturating the ADCs with voltages outside the range of Δ S , when all information would be

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95 lost. However, imagine now Δ s = 10mV, such as one might get directly from a thermocouple, for example. Note that the resolution of the ADCs in volts does not change , but as a fraction of the amplitude of the input signal, the resolution is now poorer by a factor of 100, at 24.4%. The moral of this story? Use OpAmps to bring the voltage levels up to usable values. The second reason for doing this is to avoid the potentially disastrous contamination of low level signals in an extremely noisy environment (your computer), before they are digitized. Time resolution Here is a sine wave sampled in the lab. The data points must go on intersections of the discrete mesh: e(t) t The discretisation is in both e , and t . The signal might be reconstructed from the data points in the following two ways:
96 Version 1: super-honest. e remains fixed until we know different.

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## This note was uploaded on 10/12/2009 for the course AME 341AL at USC.

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6.4 - 6.4 Properties of Discrete Signals Elementary but...

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