I am completely in the "anti-aliasing filters have no place in time domain instruments" camp:
1. If the anti-aliasing filter is going to track the sample rate or decimated sample rate, then the frequency and phase response of the oscilloscope is changing as the sample rate changes and that can happen with different record lengths. That will make for a wonderful tail about how the DSO lied to me.
The digitally-implemented version being "hi res" mode (as Tek and others used), or selectable (on screen / digital) bandwidth (mostly available on newer models?).
It's handy, but also hides things. If you want to see noise, even if it's aliased, you want "sample" mode (peaks will pop in and out as the signal and trigger jitter around), or "peak" mode if you have the excess sample rate.
Probably, the popularity of excess sample rate stems from the consistency of being able to say, yep, here's the bandwidth, here's the signal, you can see full sample rate in a single shot trigger, and you can do much more, digitally, without having to worry about incoherent signals or transients maybe being there or not.
Downside being, oh look it's a 1GS scope that doesn't even do as much bandwidth as my 100MS scope, what a waste.
2. If anti-aliasing occurs as part of decimation, then the Gibbs phenomenon is going to screw up the time domain response anyway. If the Gibbs phenomenon does not appear, then anti-aliasing was not needed. I have seen this first hand on some very expensive high end oscilloscopes when they used DSP filtering in place of analog bandwidth limiting. Oddly enough some fast vertical signal chains in analog and digital storage oscilloscopes suffer from a very similar problem that has nothing to do with digital filtering.
I'm not sure you have that quite in order, there...
- Antialiasing is the process of removing high frequency components (so the signal satisfies the Nyquist theorem), and of smoothing or interpolating between nearby samples to minimize frequency content near Fs/2. (The latter is easily seen from using an FIR filter to smooth digital samples, or for a graphical example, blurring a line slightly so it doesn't look all jagged and pixelated when drawn on a grid.)
- Decimation is the process of reducing the sample rate, so frequencies that are already present in the primary (already discrete-time) source have the potential to produce lower frequency aliases in the result. If these are filtered beforehand, the result will be representative, in as much as, the frequencies which that low sample rate can support will be present, and nothing added.
- Gibbs phenomenon is, at its root, a manifestation of marginal convergence resulting from discontinuous boundary conditions. The Fourier transform of an ideal step is an infinite series of sine waves, amplitude going as 1/N. The truncated series, however, is not a step, but approximates it, with ringing around the edge. This is, by definition, the step response of a brick wall filter.
So... if antialiasing occurs, it's because it's implemented; otherwise, aliasing may occur (that was probably just a typo). Gibbs phenomenon does not occur in any digital sampling process. It can be approximated, intentionally, when it is desirable to do so, i.e., when a sharp frequency response is desired. But it's up to the designer to specify and implement that filter, if he chooses to perform a filtering operation, in decimation or other cases.
As for analog or digital: both suffer from bandwidth, peaking and rise time versus flatness compromises, some worse than others. A good old Tek 475 is tuned for a linear-phase type characteristic -- which means its vertical signal chain must have bandwidth several octaves beyond the nominal 200MHz, no small feat. I haven't tested myself, but I understand a number of newer (TDS2k series??) scopes have been tuned for rise time instead, resulting in nasty step responses.
The filter characteristic is a design issue exclusively, it can be implemented in either domain.
Next time I get my hands on a DSO with digital triggering, I want to test this with a fast edge or high frequency sine wave.
I suspect mixing between the signal and sampling frequency do to non-linearity and sampling error in the digitizer will produce sidebands which alias thereby affecting the digital trigger among other things and anti-aliasing will not fix this. On a practical level, this should result in fast edges looking significantly noisier in time and amplitude than they really are.
The problem here as I see it with digital triggering is that the aliasing screws that up also so equivalent time sampling cannot fix it like it can on a DSO using analog triggering.
Hmm, interesting. If they've done their homework and made the analog filter cutoff sharp enough before Fs/2, it should be a null result, as one would hope.
If not, there's still digital filtering, but this can only remove already-aliased components, so they would hopefully try to keep that to a minimum so as to not kill the BW/Fs ratio even more. Which means relatively small (few tap) filters, and poor cutoff (< 40dB attenuation?) for frequencies near, say, Fs/4 to Fs/2.
So, if they were overly lazy about the analog bandwidth, they may've tried their best to patch over it digitally, but won't be able to do nearly as good a job as doing it analog.
Tim
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