4 ms·
There's no problem with doing anti-aliasing digitally later based on samples you have collected. You don't need some kind of physical analog device to do it.
by Ono-Sendai 9y ago
There's no problem with doing anti-aliasing digitally later based on samples you have collected. You don't need some kind of physical analog device to do it.
- ckocagil 9y agoOnly if you oversample to cover the entire noise frequency range.
- analog31 9y agoIndeed, and digital audio systems typically combine some sort of oversampling with digital filtering. They still need an anti-aliasing filter, but the filter works at a higher cutoff frequency and can be much simpler.
- bdowling 9y agoI think the problem is that it doesn’t make sense to digitally filter frequencies higher than 10kHz from a signal that was sampled at 10kHz.
- mikeash 9y agoThat is clearly not the case, as the article repeatedly shows. By the time you have a digital signal, it’s too late. Any noise above the nyquist frequency has already been mixed into the noise below it and they cannot be separated.
- Ono-Sendai 9y agoOk let me describe it in a bit more detail. This is what we do in high-quality computer graphics rendering. Suppose you are want to reconstruct a signal, showing only the frequencies < N hz. With an analog filter, you filter out everything above N hz. Then you can sample at the nyquist frequency of 2N hz, and then perfectly reconstruct the filtered signal. Alternatively, without the analog filter, you can take some number of samples M >= 2N. The samples are randomly placed/timed. You accumulate the samples at the 2N locations, but you weight the sample when you accumulate it with some filter function. This effectively convolves and filters the signal with a low-pass filter. Because of the random sample placement/timing, high frequencies get converted to noise instead of causing aliasing. Admittedly you are taking more than 2N samples, however you don't have to do any analog filtering, and you can still reconstruct he bandlimited signal. Your reconstruction will have some noise, but the noise will decrease as you take more samples (e.g. as M increases).
- mikeash 9y agoIf you have enough samples, then of course you can do it. The article is all about someone claiming they can do it without taking more samples. Given that was the topic at hand, I kind of assumed that was what you meant.
- Ono-Sendai 9y agoOk. I was mostly pointing out that sentences from the original article like "That filtering process, because it happens in the analog world, requires real analog hardware" are wrong or misleading.
- mikeash 9y agoI’m pretty sure “that filtering process” refers to removing frequency components beyond what your sampling rate can support.
- tmuir 9y agoMy spidey sense tingled on the sentence just previous: "Filtering means removing the high frequency components from the signal" Sure, it can mean that. To claim it always and only means that, even in the context of periodic waveforms, makes me question the authors understanding of the subject.