Support tip: How to use integrator processor?
16 Jan 2015

If you need a signal and only its derivative can be acquired, the signal can be reconstructed by using the integrator INT10a processor.

Principle

The module integrates the signal applied to the input, based on the bloc diagram shown in Fig. 1.

Fig. 1 Bloc diagram of the integrator processor

The input signal v[i] is centered by using an exponentially weighted moving average (EWMA) with smoothing factor α. The result is summed, then centered by a second EWMA with smoothing factor β.

INT10a contains two parameters that can be adjusted by the user: Integration time (Ti) and Magnitude (m).

The two smoothing factors depend on the Integration time (Ti) and the sampling interval (Te), (see reference documentation).  An equivalent practical parameter is the time constant (RC). For the two EWBAs a good approximation is:

Where the result of max function is the highest value between Ti and 100·Te.

The output gain factor (c) is equal to c= 1/m.

Examples

Fig. 2 shows a verification of INT10a by applying a square wave signal. The parameters were set at Integration time = 10 s and Magnitude = 500.

Fig. 2 Response (orange) of INT10a to a square wave input (blue).

The value of the integration time Ti is set up based on the time characteristics of the input signal.
Fig. 3 shows the recording of an EMG signal and the result for different values of Ti.

Fig. 3 Integration of a rectified EMG signal with different integration time values: G2) Input signal, G3) Ti = 0.05 s, G4) Ti = 0.001 s, G5) Ti = 0.5 s

The graphe G3 shows a good integration. The result is following well the EMG envelope for Ti = 0,05 s.  G4 shows the result for Ti = 0.001 s. The selected value was too short.
G5 shows the result for Ti = 0.5 s. The selected value was too long.

The parameter Magnitude will be adjusted in accordance with the average magnitude of the input signal.