I struggle to wrap my head around this stuff …
You and me both! The math behind filters can get very complex and quite quickly goes beyond me. Indeed, Butterworth was famous for being able to solve mathematical problems other advanced mathematicians couldn’t. The best I can manage is a basic layman’s understanding, so it could be that some of what I state below is not entirely correct in some respects. I doubt anyone here has a full understanding but some probably have a better grasp than me. With that caveat:
I’ve heard from a few knowledgeable people that a 2 pole configuration butterworth filter is “useless” as a DAC interpolation filter but good as a cross over filter, is this true?
A 2 pole Butterworth is generally fairly useless as a DAC anti-image or reconstruction filter, although not necessarily entirely useless in the case of say a reconstruction filter with a highly oversampled signal (>64x). It would be better used as a cross-over filter (and often is) but more typically a 4 pole configuration rather than 2 pole. The main benefits of a Butterworth filter (as I understand it) are better phase response than most other minimum phase filter designs (but not as good as a linear phase filter) and a reduced amount ringing but the trade-off is a requirement for a wider transition band (EG. A lower roll-off frequency).
An inherent “problem” with anti-image (and anti-alias) filters with the lower sample rates (44.1kHz or 48kHz) is the requirement for a relatively narrow transition band, in addition to the high attenuation (EG. -120dB) required at the Nyquist Frequency. So a Butterworth filter is not well suited to this application because the wider transition band would have to start well within the audible spectrum. This wider transition band requirement wouldn’t be much of an issue with a reconstruction filter for a very high oversampling rate (with a Nyquist Freq in the several mHz range) but AFAIK, is still not a favoured design even for this application.
[1] So its the black response?
[2] Still not sure why it would still be useless because if im right then apple also use this type of filter in their DACs which also sound really good.
1. It could be either, although I presume it’s the red one to indicate the reduced amount of (post) ringing.
2. Both of them are useless as anti-image filters for 44.1/48kHz, because there’s little or no attenuation at the Nyquist Freq. The black one is useless for any PCM sample frequency. The red one has 12dB attenuation for a 192kHz sample rate and obviously double that for a 384kHz sample rate but that’s still far from an ideal response!
I don’t believe Apple uses these filters or indeed any competent DAC manufacturer, the stop-band rejection is rubbish! As far as I’m aware, Apple uses “apodizing” filters. This is a rather vague term as I understand it and seems to indicate some sort of hybrid filter design, analogously like a linear phase filter “overlaid” with a minimum phase filter, resulting in a filter with minimum phase ringing characteristics but allows for a slightly narrower transition band and better phase characteristics than a purely minimum phase filter. The trade-off is latency and increased computing power, although the latter isn’t a concern these days and the former not a concern for consumers.
TBH, I’m not sure what the graph is supposed to achieve. If it’s the response of an anti-imaging filter for sample rates up to 192kHz, then both are effectively broken/faulty and I presume the point is to demonstrate the reduced ringing of the red filter to audiophiles who’ve been (falsely) led to believe ringing in response to a Dirac Impulse is a terrible evil, while ignoring the actual purpose of an anti-imaging filter, which is to “filter”!
They both look audibly transparent to me.
Really? They don’t look at all transparent to me. There’s no or virtually no rejection above the Nyquist Freq and therefore, there will be significant ultrasonic “images”. Transparency will therefore entirely depend on the downstream analogue components, how the amp and transducers respond to this relatively high level ultrasonic content. It is very likely that some IMD will occur and very possibly enough to be audible, in which case the result obviously wouldn’t be “transparent”.
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Unfortunately, this whole filter thing is just another example of audiophile marketing BS! Take a “problem” which isn’t actually a problem, because music doesn’t contain Dirac impulses, exhibits ringing rarely, at a low level and in the ultrasonic (inaudible) range anyway, and then market cures for this non-problem. These “cures are worse than the illness” and in some cases so much worse that you actually end-up with audible artefacts, although of course you can then market that as (somehow) more “musical” and some/many audiophiles will be deliriously happy to pay more for a crappy converter!
G
