Filtering Overview

Filtering is used to remove unwanted frequency content. The enDAQ analyzer provides a variety of filter options that will be discussed in this article to understand what filter is best for your application and how they can be useful.

In this Article


Why Filters are Helpful

High-pass filters remove lower frequency vibration and is inherent to all piezoelectric accelerometers (resistor and capacitor in series) which gives these accelerometers the AC response (for more information on accelerometer types check out our blog on accelerometer selection). This is useful for filtering out DC bias and the drift that can often occur due to temperature change.

Low-pass filters are more important however to prevent aliasing which can’t be filtered out in software. Aliasing causes a signal to become indistinguishable or to look like a completely different signal as shown below. It’s important to realize that an analog lowpass filter is needed to prevent aliasing. Once a signal is aliased, it can’t be filtered out digitally in software.  Low-pass filters can also filter out unwanted higher frequency content that may be related to structural modes that aren't relevant to your application.  Higher frequency vibration content also typically has less energy than lower frequency content.

aliasing.bmp

Filter Types

Now the question remains as to what type of filter should you use? An ideal filter would uniformly pass all frequencies below a specified limit and eliminate all above that limit. This ideal filter would have a perfectly linear phase response to the same upper-frequency limit. But ideal filters don’t exist; there is some compromise that needs to be made on a filter’s amplitude and phase response. There are four main different types of filters:

Butterworth

A Butterworth filter is known for its maximally flat amplitude response and a reasonably linear phase response. The Butterworth filter is the most popular for vibration testing.

Bessel

The Bessel filter has nearly perfect phase linearity so it is best suited for transient events like shock testing. It has a fairly good amplitude response but its amplitude roll-off is slower than the Butterworth or Chebyshev filter.

Chebyshev

The Chebyshev has a faster roll-off in the amplitude response which is achieved by introducing a ripple before the roll-off. They have a relatively nonlinear phase response.

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.


Filter Comparison

The performance of these filters are compared for a 1,000 Hz cut off frequency and 5th order filters. 

bessel-butterworth-chebyshev-elliptical-filter-comparison-5xFc-1.svg

The following plot 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!

bessel-butterworth-chebyshev-elliptical-filter-comparison-passband-2.svg

Note

Notice how all the filter types begin attenuating the signal before the cut-off frequency. This is because the cut-off frequency of a filter specifies when the attenuation has reached -3dB which is nearly -30%!


Example with Real Data

To illustrate how different filters can influence the real data and in different ways, let's look at some data recorded from a Slam Stick.  

Vibration

This data is from a test where the jet aircraft cargo vibration was generated on a shaker and then recorded with a Slam Stick.  The raw data and some more information about the test is available to download in our community forum.

Let's take a look at the raw data without any digital filters applied and the accompanying PSD.

Now let's apply an 8 order Butterworth filter at 100 Hz and take a look at the PSD.

Here's an Elliptic filter, one can notice the sharper cutoff but then accompanying ripples.