It is sometimes necessary to perform high pass filtering to eliminate low frequency signals. These may arise for instance from whole body vibrations when perhaps our interest is in higher frequency components from a substructure such as an engine or gearbox mounting. The vibration levels are speed sensitive and the usual scheme is to record a once per revolution ‘tacho’ signal with the vibration data. The tacho signal, which ideally is a nice regular pulse train, is processed to find rotational speed and hence to select which part of the vibration signal is to be frequency analyzed. The most common form of analysis is a waterfall type such as shown below.
Suppose now we need to eliminate the low frequencies. This is quite simple as all we need to do is to perform high pass filtering on the vibration data. Because normal filtering causes a time delay then we must also filter the tacho signal. Conventional wisdom is that if all signals are filtered the same way then the effects of time delays may be ignored as they are all the same relatively. This, however, ignores the time domain effect on the signals, which is important for tacho signals.Processing a tacho signal is essentially based on determining the time interval between successive rising edges as illustrated for the ideal tacho shown below.
If each pulse represents one revolution then the speed between the two successive pulses is clearly (1/T). A real tacho pulse is rarely as clean as above. The figure below is a typical tacho signal measurement. In fact, as far as tachos go the example is quite a good quality tacho.
Because of the effects of noise we need to choose a threshold amplitude level as our trigger point to determine the time interval between successive pulses. If the tacho goes between Vmin and Vmax then generally a suitable threshold level is (Vmax+Vmin)/2.
Suppose now we need to high pass filter our data to eliminate some low frequency characteristics. Applying the same filter to the tacho may cause some dramatic effects. The example below is the tacho signal above filtered with a simple 4 pole high pass Butterworth filter set at 5Hz. This is a well behaved non aggressive filter but its effects on the tacho waveform are quite significant.
Whilst we have the same average temporal delays the detail effects are such that we may run into serious difficulties in selecting a trigger point. It could be as much as half a revolution in error if we used a negative level on the positive slope port. As the high pass filter is set to a higher cut off then the resultant tacho becomes totally invalid. For example, using a cut off of 35Hz on the original tacho gives a result which would indicate the engine was running at twice the speed. As shown below the tacho is now almost unrecognisable!
The solution is to use phaseless filtering. This gives no time delay effects as there is zero phase. Applying a phaseless 4 pole high pass Butterworth with a 35Hz cut off gives a signal which is almost identical to the original. The dc level and other low frequency components have been removed without the harmful time delay distortions, the filter is no longer acting as differentiator.
Chief Signal Processing Analyst (Retired) at Prosig
Dr Colin Mercer was formerly at the Institute of Sound and Vibration Research (ISVR), University of Southampton where he founded the Data Analysis Centre. He then went on to found Prosig in 1977. Colin retired as Chief Signal Processing Analyst at Prosig in December 2016. He is a Chartered Engineer and a Fellow of the British Computer Society.