CoCo-80 User Manual
97
Calculation Errors in Digital Integration
Two types of calculation errors can be caused by digital integration: low sampling
rate and DC offset.
The sampling rate of a signal must be high enough so that the digital signal can
accurately depict the analog signal shape. Some people may think that according
to the Nyquist sampling theorem as long as the sampling speed is more than twice
of the frequency content of the signals before the integration, the integration
results should be acceptable. This is not true. Satisfying the Nyquist frequency
only ensures an accurate estimate of the frequency of a measurement. Integration
error can still occur of a signal is not sampled at more than twice the signal
frequency. Figure 106 shows a 1 kHz sine wave sampled at 8 kHz and 5.12 kHz.
Figure 106. A 1 kHz sine wave sampled at 8 kHz (top) and also sampled at
5.12 kHz (bottom).
It is clear that the higher the sampling frequency, the closer this digitized signal is
to the true analog waveform. When the sampling rate is low, the digital
integration will have significant calculation error. For example the 5.12 kHz
sampled signal is not symmetric about 0 volts so the integration will drift and a
double integration may grow with accumulated error very fast.
In general, you should use a sampling rate 10 times higher than the frequency
content that is of interest in the signal when you apply numerical integration.
DC offset is the second type of digital integration error and can be more severe. It
is caused by any measurement error before integration and may result in huge
amplitude errors after the integration. Figure 107 shows how a small
measurement error in acceleration will create a constant DC offset in the
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