24
where
1
s
T
F
=
,
s
F
is Sampling Frequency. RealWave uses the
“
Forward Euler
”
method, which is
simplified from Trapezoidal Method. We can write it as below :
( )
1
1
1
Tz
H z
z
−
−
=
−
<Eq.
IV-1-7>
The frequency response function of integrator is shown in the [Fig. IV-1-6].
[Fig. IV-1-6] Frequency Response of Forward Euler Integrator
[Fig. IV-1-7] Integrated Result
Discrete integrator generates offset of signal (see [Fig. IV-1-7]). We must use highpass filter for
removing the offset. The highpass filter with 10Hz cutoff frequency (2-pole Butterworth IIR Filter) is
used in RealWave. The procedure for velocity and displacement is shown in the [Fig. IV-1-8]
Integrator
Highpass filter
(10Hz)
Integrator
Highpass filter
(10Hz)
Acceleration
Velocity
Displacement
[Fig. IV-1-8] Flow-chart for integration
Discrete integrator has original error as shown in the [Fig. IV-1-9]. Specially, that error increases
Summary of Contents for SLA-PA201
Page 64: ...64 Appendix 1 The Theory for calculating RMS by ISO2631 and ISO8041 ...
Page 67: ...67 Appendix 2 Frequency Response of Filter in the Vibration Level Meter ...
Page 75: ...75 Appendix 3 Theory of WBCombined Filter and Frequency Response ISO6954 Filter ...
Page 79: ...79 Fig 2 Lowpass Filter with 100Hz Cutoff Fig 3 a v transition Frequency Response ...
Page 88: ...88 Fig 12 Error between theoretical value and measured value ...
