Simcenter Testing Solutions Acquisition Filters and Overshoot

Acquisition Filters and Overshoot

Applying filters (for example low-pass anti-aliasing filters) to time data can create overshoots.  When a sudden change in amplitude occurs in a time signal, the filter can cause a noticeable variation in amplitude as shown in Figure 1.  This is caused by the removal of frequency content from the original signal.
 

This overshoot might need to be addressed depending on how the data will be analyzed:

1. Time Domain versus Frequency Domain

In frequency domain analysis, time data is converted to the frequency domain by Fourier analysis.  The analysis can be performed without much of a worry because the overshoot effect is broad in frequency but causes a very small change (or none depending) in the amplitude of the frequency domain. 

In data acquisition and analysis, the amplitude in the time domain matters.  Examples of time based testing and analysis include shock testing, road load data acquisition, and transient analysis. These time data measurements need to be just right: statistics, peaks, times at level, level crossings, range pairs, rain flows, and logical triggers all depend on accurate amplitude time data (Figure 2).
 

Just small changes in the amplitude can change fatigue life estimates drastically.  See this knowledge article for more information: What is a SN-Curve?.

2.   Set Measurement Bandwidth Correctly

The information of an analog signal is contained in its bandwidth, aka its frequency content (both in magnitude and phase). Most analog signals have a bandwidth between zero Hertz and some frequency (aka bandwidth of interest). Two situations are possible based on the analog signal frequency content versus the measurement bandwidth setting:

2.1   Nyquist-Shannon

Following Nyquist-Shannon sampling theorem and its hypotheses, if the digital data is acquired with a sample rate higher than the double of the signal bandwidth, all the information of the original analog signal will be correctly digitized/encoded, and even perfectly reconstructed if necessary. In other words, if the analog signal bandwidth is below of half of the sample rate (aka Nyquist frequency) then no artifacts are possible.
 

2.2   Why Is A Filter Needed?

Unfortunately, analog signals often have signal content greater than the bandwidth used to digitize the data.  This can cause undesirable noise (aliasing) to occur as the higher frequency signals "foldback" into the measurement bandwidth as shown in Figure 3.
 

Think about the input signal as a combination of actual expected signal and undesired noise. Acquisition low pass filters (from now on, just filters) are then needed, to mold the input signal into a smaller bandwidth, and more importantly, to get rid of noise and alias frequencies.

More about sampling rates, bandwidth, and aliasing in these knowledge articles:

3.   Choosing The Right Acquisition Filter

Both for frequency and time domains, there are two options: either set the measurement bandwidth high enough to capture the entire analog content of the signal, or choose the acquisition filter type appropriately. For the second choice, depending on the filter type used, overshoot in the time data might appear more, less, or not at all.

3.1  Why You Should Care About Your Filter

The measurement bandwidth is defined by the filter passband, or cut-off frequency (Fco), generally at -3dB (Figure 4).

Figure 4: A filter is defined  by a pass-band, transition band, and stop band.  The cut-off frequency (Fco) delineates the pass-band and transition band, and is usually defined at the 3dB attenuation point of the pass-band.
 

Implementable filters aren’t ideal:

Figure 5: Comparison of magnitude frequency response of different filter types.
 

All of them optimize certain attributes at the price of compromising others.

 

Figure 6: Filter roll-off performance versus order. The higher the order (for the same filter), the greater the roll-off.
 

Increasing the order increases the roll-off, but compromises filter complexity and process delay.

More about filters in the knowledge article: Introduction to Filters: FIR versus IIR

3.3  Phase: As Linear As Possible

Classical analog and digital IIR filters have non-linear phase responses (Figure 7) because they are intrinsically causal. Each signal frequency component won’t propagate through the filter with the same time delay.
 

Figure 7: Non-overshooting non-linear filter effect.
 

Delay is an undesirable artifact of a filter.  Filters have existed for years (especially the analog ones), so their behavior is well known. Furthermore, IIR filters are easy to design: they are cheap, simple, and very performant. However, they exhibit non-linearity in their phase responses. In the time domain, this produces scattering (or asymmetries).

Phase linearity in the passband means that group delay (proportional to the derivative of phase) is as constant as possible.  This ensures minimal shape distortion and helps distributing overshoot, if any, before and after transients.

In general, increasing filter order reduces phase linearity (Figure 8).
 

 

But there are exceptions where phase linearity improves with filter order, like Bessel and transitional filters like Gaussian.

Finally, only a subset of synthesized digital Finite Impulse Response (FIR) filters can have exactly linear phase transfer functions. If possible, use a linear phase FIR filter when collecting data. The Simcenter SCADAS hardware has both sharp and smooth linear filters choices.

3.4   Magnitude: Ideal For Frequency Might Not Be For Time

If the measurement bandwidth is not high enough relative to the signal frequency content, information will be lost after filtering. The best filtered version for time analysis (smooth in time), is not necessarily the best version for frequency analysis (overshooting in time). Differences between some filter types and their orders are shown in Figure 9.
 

Good news is that an acquisition filter can be selected to tune how it impacts the measurement. This is especially helpful for the time domain when overshoot comes into play.

3.5 Cause Of Overshoot

Overshoot is a product of a sharp filter impulse response magnitude, when there is frequency content falling into the stopband as shown in Figure 10.
 

Figure 10: As signal (green, left) is passed through a filter (middle) it can result in overshoot being added to the signal (right).
 

There is an actual need to store stopband energy in the filter itself, and it may be abruptly released and overlapped later into the passband. As a rule of thumb:

3.6 Signal Overshoot Is Not Gibbs

The Gibbs Phenomenon is commonly confused with data acquisition artifacts, like overshoot. Although the result resembles in both cases a ringing artifact, while overshoot may (or not) be produced after filtering a signal, Gibbs phenomenon always appears after approximating a discontinuous function with a finite set of its Fourier Series (Figure 11).
 

Overshoot is a physical product of a filter, Gibbs is a mathematical consequence of a suboptimal approximation exercise.

3.7    Sharpness Versus Smoothness

If the signal frequency content goes beyond the measurement bandwidth, sharpness is desired for frequency domain transition band, allowing more efficient usage of outhe measurement bandwidth given a sample rate.

On the other hand, smoothness is better for time domain, allowing smoother energy release; thus, overshoot is minimized and eventually avoided. Sharpness depends only on the filter type (Bessel, Butterworth, Cauer, etc). Smooth and sharp filters are shown in Figure 12.
 

Figure 12: Sharp (left) versus smooth (right) filter shapes.
 

To achieve better stopband attenuation figures using a smooth anti-aliasing filter, extra care should be taken to use higher sample rates so that Nyquist frequency gets pushed safely above cut-off frequency (Fco).

The time domain differences and frequency domain differences between sharp and smooth filters are shown in Figure 13.
 

Figure 13: A sharp filter (elliptic, upper left) in the frequency domain results in overshoots in the time domain (upper right).  A gradual, smooth filter (Bessel, lower left) has no overshoot (lower right).
 

A sharp filter (elliptic) has a narrow transition band in the frequency domain.  However, the sharp filter results in overshoots in the time domain.  A smooth filter (Bessel) has no overshoot in the time domain, but has a more gradual attenuation performance in the frequency domain relative to the sharp, elliptic filter..

4.  Real World Signals Are Not Square Waves

There are many types of signals in the real world, not all of them are square waves.  Consider the real world transient signal shown in Figure 14:
 

The signal has significant frequency content up to 17 kHz as shown in Figure 15:
Assume the signal needs to have high frequency content (above 11 kHz) to be removed. A "sharp" filter might be used. For example a 14th order Butterworth low-pass filter as shown in Figure 16.
 
It might be expected that removing signal content would result in smaller amplitudes in the filtered signals.  However, due to overshoot created by the Butterworth filter, some of the amplitudes have increased as shown in Figure 17:
 

6.  Conclusion

Some conclusions: