When this analog value is represented as a digital number, however, this essentially continuous resolution is limited to discrete steps. Resolution of A/D conversion often is stated in bits—the more bits the finer the resolution. The number of bits also determines the number of divisions into which a full-scale input range can be divided to approximate an analog input voltage. For example, 8-bit resolution of a 0-10 V input signal means that the range is divided into 28 or 256 steps. This yields a step, or interval, size of 10 V/256 = 0.039 V. A 10-V input is equal to the digital number 255 and a 0-V input corresponds to 0. Each 0.039-V change in the input is indicated by adding or subtracting 1 from the previous number, so 9.961 V is digitally represented as 254.
The paper reminds us that digital data acquisition systems also parcel time into discrete intervals. There really is no information about the behavior of the variable between data points gathered. Special precautions are needed to prevent meaningful data loss, so the interpolation between recorded points will remain a valid assumption.
The Nyquist Theorem defines the necessary relationship between the highest frequency contained in a signal and the minimum required sampling speed. Nyquist stated the sample rate must be at least twice the highest frequency component contained in the input signal. To sample a 1-Hz sine wave, the sample rate should be at least 2 Hz. But a rate of 8-16 Hz would be much better for resolving the true shape of the wave.
The primary implications of ignoring the Nyquist criterion include missing high frequency information and introducing aliasing. If the sample rate isn’t sufficient, the presence of nonexistent frequencies might be indicated. Aliasing makes helicopter rotors or car wheels appear to turn slowly backwards in movies. Low-pass or anti-aliasing filters can be used to limit the measured waveform’s frequency spectrum, so that no detectable component equals or exceeds half of the sampling rate.
Designing or specifying a device for A/D conversion consists of a series of tradeoffs. More resolution means more accurate conversion but more expensive hardware. Similarly, slower sample rates mean cheaper A/D conversion, but the Nyquist criterion must still be satisfied.
AN ALIAS IS NOTHING BUT TROUBLE |
|