Time-Domain Integration

Time-domain integration is a technique used to determine displacement and velocity from acceleration data. You can use integration to convert acceleration data to displacement data in a single-shot acquisition and integration.

Because the integration is implemented with filters, there is a transient response associated with integration while the filters settle. You must avoid the transient region when making further measurements. The following figure shows the results of a single-shot acquisition and integration of a 38 Hz sine wave.

Figure 15. Single-Shot Acquisition and Integration

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You can see the transient response in the first 200 ms of the integrated signal.

The more common case for time-domain integration occurs with continuous acquisition. The following figure shows the results of the continuous acquisition and integration of the same 38 Hz sinusoid used in the single-shot acquisition and integration example.

Figure 16. Continuous Acquisition and Integration

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As in single-shot acquisition and integration, continuous acquisition and integration has an initial transient response. Do not make additional measurements until the response of the filters settles. Once the filters settle, you can use the integrated signals for additional analysis. Typical settling time is given by the following equation: T_settling = 5 / high-pass cutoff frequency.