Page 18 - Shock and Vibration Overview

Data Acquisition (DAQ) System Selection

4) Elliptic
The Elliptical filter has the steepest roll-off in the amplitude response but it has a
ripple in both the pass band and stop band. In addition, its phase response is highly
nonlinear. This is only used for applications where phase shift or ringing is not of a
concern; it should generally be avoided to the common test engineer because of its
tendency to distort complex time signals.

In Figure 8 the performance of these filters are compared for a 1,000 Hz cut off
th
frequency and 5 order filters. The plots were generated in MATLAB using the Signal
Processing Toolbox and the analog filter functions. Figure 9 takes a closer look at the
filter performance in the passband (0 to 1,000 Hz). The Chebyshev and Elliptical filters
offer that sharper amplitude roll off but at the expense of large ripples in the passband

and nonlinearity. Butterworth filters offer the best of both worlds with a relatively sharp
amplitude roll off. Bessel has the best phase response and a reasonably good amplitude
response but note how early it begins filtering; and in the stopband it still allows over
10% of the single until roughly 2.5x the cut off frequency.

Figure 8: Different filter types are compared on their amplitude response and phase for a 1,000
th
Hz 5 order filter.

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