Page 65 - Prosig Catalogue 2005

SOFTWARE PRODUCTS
THE BASICS OF DIGITAL FILTERING

will remove the frequency content above 100Hz, but not below 100Hz. It
follows that a sinewave with a fundamental frequency of 10Hz would not
be affected by a 100Hz low pass filter. But a sinewave of 200Hz would be
heavily affected by a low pass 100Hz filter as the frequency content above
100Hz would be removed.
High pass filters are the opposite to low pass filters. They remove the
frequency content below the cut off frequency.
Band pass filters will have a low and high cut off and will pass frequencies Training & Support
that fall between these two limits.
Band stop filters will block the frequency content between the lower cut
off and the higher cut off.
We call the rate at which the filter attenuates the frequency content, the
roll off rate. The filter cut off point for a low pass filter of 100Hz does not
mean that the filter begins to work at 100Hz. This means that the filter Figure 7: Characteristics of 250Hz to 750Hz band pass filter
will have attenuated the signals amplitude by about 30% at that point.
This is known as the filter 3dB point, where the energy or power of the
signal has reduced by 50% (and the amplitude reduced by a factor of
0.7071). The ‘rate’ of the roll off is measured in attenuation per frequency
(dB per octave). This is the number of dB being attenuated per frequency
octave, where an octave is a doubling of frequency.
Figure 5 shows the characteristics of a low pass filter, this example would Condition Monitoring
allow the low frequencies to pass but block frequencies above 500Hz.

Figure 8: Characteristics of 250Hz to 750Hz band stop filter
applied any filtering. This swept sinewave starts at 1Hz at t=0 seconds
and increases to 1000Hz (or 1kHz) at t = 5 seconds.
Figure 10 shows the full swept sine wave after we have applied the Low
pass filter. We can see how the signal is unaltered initially, but as the
frequency approaches, and passes, the 500Hz cut off we attenuate more Software
and more of the signal.

Figure 5: Characteristics of 500Hz low pass filter
The high pass, shown in Figure 6, would block frequencies below 500Hz,
but allow frequencies above 500Hz.

Hardware

Figure 8: Characteristics of 250Hz to 750Hz band stop filter

Figure 6: Characteristics of 500Hz high pass filter

The band pass, shown in Figure 7, would block frequencies below 250Hz,
allow frequencies between 250Hz and 750Hz, then block frequencies
above 750Hz.
The band stop filter, shown in Figure 8, would allow frequencies up to 250 System Packages
Hz, block frequencies between 250Hz and 750Hz, but allow frequencies
above 750Hz.
Which poses the next question - how would a swept sine wave be affected
by these different filters? Figure 9: Swept sinewave before filtering
Figure 9 shows the first 5 seconds of the swept sine wave before we have

http://prosig.com +1 248 443 2470 (USA) or contact your 65
sales@prosig.com +44 (0)1329 239925 (UK) local representative
A CMG Company