Anti-Alias Filtering
Until Synergy, the filtering needs for a traditional FFT analyzer and scope were very distinct. Almost all competitive instruments are designed to favor one domain or the other, and therefore will exhibit large and uncorrectable errors in half your applications.
The steep rolloff required to maximize FFT performance causes a large overshoot in Time Domain step response. Conversely, the wide bandwidth required for good waveform fidelity in DSO applications is poorly suited for FFT use due to aliasing in the frequency domain.
The waveform in Figure 1 below is a 1 kHz square wave as reproduced through a steep FIR filter or sigma-delta converter. The distortion, called Gibb’s phenomenon, is so severe as to make the square wave almost unrecognizable. While it seems counter-intuitive that a filter could “add” oscillations, recall that in theory a square wave is constructed of an infinite series of harmonic sine waves. The overshoot effect is actually caused by phase non-linearity and the lack of the higher frequencies which would “fill in” the ripples.
Fig. 1: In most recorders & FFT analyzers,
a square wave is badly distorted by sigma-delta type filters
On the other hand, the wide bandwidth required for good waveform fidelity on your DSO is poorly suited for FFT use due to aliasing in the frequency domain. The waterfall in Figure 2 is the FFT of a square wave beginning at about 10 kHz and sweeping upward in frequency. Since a square wave’s harmonics extend to infinity, the components above 100 kHz are “folded back” into the spectrum and falsely appear as lower frequencies. For example, the 11th harmonic at 110 kHz appears in the display to be 90 kHz. All the spectrum ridges that lean to the left are alias frequencies that did not exist in the original signal.
Fig. 2: In most DSOs, the FFT of a square
wave contains many false alias frequencies
Rather than permanently compromise one mode like competitive instruments, Synergy offers software selection of filter characteristics to best suit your varying tests. The following examples show when to use each type.
Figure 3 below shows a linear frequency sweep increasing to 100 kHz. As seen in the upper plot an oscilloscope-like time-optimized filter gradually attenuates the signal beginning at a low frequency, increasing to -3 dB (a 29% amplitude error) at its cutoff frequency. Even frequencies at 1/10th the 3 dB point are reduced in amplitude by several percent. In contrast, the steep-cutoff FFT filter provides very accurate amplitude readings up to 80 kHz but strongly attenuates all signals above 100 kHz to avoid aliasing. When you need the flattest frequency response such as for modal analysis or acoustic studies, always use the FFT filter type.
Fig. 3: FFT filter has flatter, more accurate
frequency response
Figure 4 shows a square wave input, the classical test of an oscilloscope’s quality. An accurate square wave requires a wide, smooth bandwidth with gentle roll-off. In this case notice the time-domain filter is much more accurate when you zoom in on the edge. The more aggressive FFT filter causes overshoot and aberrations that did not exist in the signal. When you need accurate peak measurements on a fast signal such as a ballistics signal, an actuator response or an engine combustion waveform, always use a time-domain filter and the highest possible sample rate. Systems which use sigma-delta A-D converters are unsuitable for this class of measurements and can lead to large uncorrectable errors.
Fig. 4: Time filter has more accurate step response
Left in the “Auto” mode, Synergy’s filters provide automatic anti-aliasing protection of the optimal bandwidth for all sample rates. Manual selection of filter frequencies is also provided to further clean up noisy signals.
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Synergy Hi-Points
- Key Features
- Architecture
- Anti-Alias Filtering
- Universal Signal Conditioning
- ClearVU Display Technology
- Binary and Decimal Sampling
- Analysis and Report Generation
- The Ethernet Advantage
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