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Post by petea on Dec 5, 2019 15:09:13 GMT
Something has been niggling at me for a while and it probably comes from me not understanding the Fourier transforms used (at all), but it is hinted at in the first and last waveforms shown in the video and referred to by a poster on page 25 of the Head-Fi thread.
"I find it disturbing when people describe the Nyquist theorem like this. The theorem really only holds if all past and future samples are available or that the signal be periodic (which then happens to provide said past and future signals by virtue of repetition). There is no real guarantee that in other cases the waveform (function) will be re-created. Integration from -infinity to infinity is integral part of the theorem. In fact, for any k point sample size you will be able to find infinitely many functions that are not precisely reproduced despite having no frequency component above fs/2. The Nyquist theorem gets abused way too much - having to deal with just past samples or a limited set of samples or quantization sets different limits than Nyquist.
However, its also true that DAC-s do produce fairly good reproductions of the initial waveforms up to frequency of fs/2 ... but tat is rather despite than thanks to the Nyquist theorem that really sets the limits in this case, rather than providing guarantees."
It's that periodicity bit. If the waveform of the musical source is complex, has asymmetries in it and overlapping transients then surely a higher sampling rate will result in a more faithful reconstruction than a lower sampling rate (up to the point at which artefacts become a problem). So maybe 96K files should have better fidelity than 44K ones - and I think they are only available in 24 bit depth in any case. There are papers on modifications to the theorem that demonstrate that varying the frequency of the sample rate improves reconstruction of 'non-standard' wave forms which suggests to that there must be issues. As to how audible these are I cannot say.
Addressed on pages 281 and 282.
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Post by MartinT on Dec 6, 2019 6:51:32 GMT
To a degree, bit-depth and sample rate are interchangeable (the extreme being DSD which is 1-bit 2.8M sample rate). I have noticed more 24/44.1 files becoming available in Qobuz recently, and they tend to sound good even if the format (Red Book but with a higher bit depth) seems strange at first.
Remember also, that with any given format there are different ways that a DAC can re-create the waveform from the data, depending on what balance of attributes you choose. Some DACs allow this setting to be changed. I have for a long time preferred Minimum Phase as it preserves the leading edge of transients while sacrificing the waveform integrity slightly after the transient. This, to my ears, sounds more dynamic and improves soundstaging.
I will personally go back to: jitter reduction is more important than the digital format used. The processing chain, re-clocking for jitter reduction and cable quality used all play a part. You can achieve very impressive sound quality from 16/44, but higher resolutions can sound even better.
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Post by nrg on Dec 6, 2019 9:20:36 GMT
Martin bit rate and sample rate are not interchangeable! Great thread BTW....
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Post by jandl100 on Dec 6, 2019 9:45:34 GMT
I'm fairly well educated in physics, but I have to confess I am left baffled by digital sampling once you dig deep enough for the details to matter. I suspect most folks are, actually, even though they may not realise it!
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Post by MartinT on Dec 6, 2019 10:17:44 GMT
Martin bit rate and sample rate are not interchangeable! Great thread BTW.... Hmm, I seem to remember that they are, at least on a theoretical level.
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Post by MartinT on Dec 6, 2019 11:41:51 GMT
Comparative Bitrate Calculations Format | Bit Depth | Sample Rate | Bit Rate | CD Red Book | 16-bit | 44.1kHz | 1411Mbps | Hi-res | 16-bit | 48kHz | 1536Mbps | Hi-res | 24-bit | 44.1kHz | 2116Mbps | Hi-res | 24-bit | 88.2kHz | 4234Mbps | Hi-res | 24-bit | 96kHz | 4608Mbps | DSD (SACD) | 1-bit | 2.822MHz | 5644Mbps | Hi-res | 24-bit | 192kHz | 9216Mbps |
I've just knocked up the above table to see how the Bit Rates look and where standard DSD sits in comparison with PCM. For example, 24/96 in real terms has around 3.3x the 'resolution' of standard CD and DSD has 4x.
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Post by liffy99 on Dec 6, 2019 13:56:04 GMT
I'm fairly well educated in physics, but I have to confess I am left baffled by digital sampling once you dig deep enough for the details to matter. I suspect most folks are, actually, even though they may not realise it! I do feel sad for you lesser mortals - I actually know EVERYTHING which can be confirmed by my wife !
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Post by MartinT on Dec 6, 2019 14:15:16 GMT
When my son was 16 I apparently knew NOTHING. Somehow I have stumbled through life meanwhile...
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Post by MikeMusic on Dec 6, 2019 14:20:54 GMT
The more I learn the more I find don't know !
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Post by nrg on Dec 6, 2019 14:49:23 GMT
Martin bit rate and sample rate are not interchangeable! Great thread BTW.... Hmm, I seem to remember that they are, at least on a theoretical level. Not really, bit depth is the number of bits in the sample, sample rate is how many times a second you sample at and bit rate is the product of the two. You can’t interchange the terms without causing a load of confusion!
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Post by Deleted on Dec 6, 2019 15:11:15 GMT
Do not forget the higher sample/bit rate the more data is required to store this music normal CD is around 780-800Mb. Some of the music we record can be as much as 4-8Gb per track depending on sample and bit rates.
Hence why our music collection is 476Tb lol
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Post by petea on Dec 6, 2019 15:20:45 GMT
Yes, and that was one of the factors that resulted in the 16/44.1 bit depth and sampling rate standard chosen for CDs. I thought it interesting that the frequency used is in part to encompass the range of frequencies that most humans can hear while accommodating the requirements of the Nyquist limit and the 'decay slope " of the high band pass filter used, but also to match the DAT standard recording frequency available at the time.
Luckily storage and transmission is much less of an issue these days.
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Post by MartinT on Dec 6, 2019 17:55:45 GMT
Not really, bit depth is the number of bits in the sample, sample rate is how many times a second you sample at and bit rate is the product of the two. You can’t interchange the terms without causing a load of confusion! That wasn't quite what I meant. I was trying to say that you can, within reason, balance bit depth versus sample rate differently and get similar results. Of course you can't use a sample rate of 1Hz for audio, but there is a good example in the table above... 24/96kHz, a popular hi-res format, gives a bit rate of 4608Mbps. 1/2.8MHz, DSD, gives a bit rate of 5644Mbps. Who would have thought, before Sony/Philips brought it out, that 1-bit for audio could possibly work? Yet to my ears SACD and 24/96 both sound very good, a little different from each other, but of a similar quality level.
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Post by liffy99 on Dec 8, 2019 18:27:33 GMT
Martin bit rate and sample rate are not interchangeable! Great thread BTW.... Hmm, I seem to remember that they are, at least on a theoretical level. I think Martin is right on this one, although interchanging them does not necessarily improve anything per se (but different converter types may be easier to build accurately than another). i found the following article really helpful, and also covers the issue of jitter which was mentioned earlier. the gist of the article though is that there is nowt wrong with the theory of digital encoding and playback, but the engineering has, until recently, been playing catch up. Perhaps explained why some of those early digital recordings and CD players sounded poor. www.soundonsound.com/techniques/digital-myth
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Post by John on Jan 14, 2020 14:57:31 GMT
I thought I summarise everything I have done to improve sound quality in the digital domain Power Good mains cables throughout A modified distribution power conditioner with Shunko plugs 1 orange fuse on the cable powering the conditioner and 2 AMR fuse to the Temple Monos 3 power supplies all using supercaps 1 coherent supplying the Tinkerboard and Router 2 Superchargers for the Temple Monos External noise from a factory close by I turn off the system during the day is a simple solution to decreasing mains bourne noise when I listen in the evening. Cabling After reading peoples experience with better USB cables I changed my USB cables. Yes this did make a difference in my system Paying attention to avoiding cross-talk between close running cables Using a decent Ethernet cable with a Lan Isolator Jitter devices and grounding Boxes Both help to lower the noise floor I am experimenting trying to find out what works best for me Reclocking A nice upgrade for not crazy money BR feet on everything A few snap chokes on leads Most of these should be seen as having a cumulative effect. none are night and day, but it all adds up.
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Post by MartinT on Jan 14, 2020 15:52:43 GMT
Most of these should be seen as having a cumulative effect. none are night and day, but it all adds up. That's been my experience too, John.
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