Poll: Are perfect 1:1 copies possible in the digital domain?

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Comments

  • cfrizzcfrizz Posts: 13,397
    edited June 2014
    steveinaz wrote: »
    You guys give the phrase "wrapped around the axle" a whole new meaning. Stop "geeking" on go listen.

    ROTFLOL!!! Thank you Steve for my Friday night laugh! Truer words were ne'er spoken!
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  • BlueFoxBlueFox Posts: 11,488
    edited June 2014
    Yes, perfect 1:1 digital copies are possible. In fact, it is more than possible. It is the norm. Of course, the potential for errors is there, but the technology has matured to the point where it would take a stray neutrino to create an error.
    Bud - Silicon Valley

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  • headrottheadrott Posts: 5,428
    edited June 2014
    villian wrote: »
    Is a digital music file able to be copied perfectly (Resulting in a 1:1 copy) to another location?


    Just doing a quick survey. Feel free to state your opinion and why it is that way in the following posts. Also, if you believe that 1:1 digital copies are not possible and are willing to post about it, can you please explain what the difference would be between the source file, and the resulting duplicate file. This is assuming that the resulting file has passed all error checks and is a complete, ready to use, copy of the original. Regardless of transfer or copy method.
    The other way to ask this: Are 1:1 bit perfect digital copies impossible?

    My answer (which includes a rhetorical question) is: at what resolution are you analyzing and determining a "perfect" 1:1 digitally copied file when transferred? As was demonstrated by Ray's example in the "other" thread that the voltage pulses that correspond to a "1" or a "0" or a "high" or "low" can be transmitted and analyzed digitally as a "perfect 1:1" copy of the original source, but in fact the voltages are not the same as the orginal source material. They may be slightly higher or lower than the original material ("data source").

    These alterations to the voltage pulses are caused by different types of introduced noise (Electrical fast transient noise being an example). Also, things such as materials that these electronic pulses are transferred through can cause alterations to these voltages. Remember how much different PCOCC looks compared to TPC (Tough pitch copper)? As far as the computer is concered, the analyzed data pulses (despite being higher or lower than the original voltages sent through the cable and other parts of electronic equipment) appear to be "perfect" since as far as the computer is concerned they are either a "1" or a "0". When in fact, they are actually (to a greater or lesser degree) altered voltage pulses making up those "1's" and "0's" or "high" and "low" states.

    A person can listen with their ears and potentially determine that the altered voltages are in fact, not "perfect 1:1" digital copies of the original material while the computer simply sees the altered voltages and still demarks them as a "1" or a "0" making them apppear to be "perfect". Again, there is absolutely no perfect transfer of energy using the technology we possess; there is always loss to a greater or lesser degree. Always.

    So, no to your question villian and yes to your question Habanero Monk.

    Edit: I should specify in the answer to Habanero Monk's question that what the computer considers "bit perfect 1:1" files are possible because the computer still considers them a "perfect" "1" or "0". But the voltage pulses used to create those "1's" and "0's" were not perfect. So the answer is still yes to a person listening to the copied material (depending on the variation the voltage pulses of course). Once there is enough variation in the voltage pulses, the differences become much more obvious to a listen but still appear to be "perfect" 1's and 0's by the computer.

    I should also specify that it is these variations in voltages pulses that make up the noise in digitally copied material and also are what make up what is heard by the listener ( a less than perfect source).

    And Steve, I listen just as much as I go on a "geeking" spree. :smile:
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    Taken from a recent Audioholics reply regarding "Club Polk" and Polk speakers:
    "I'm yet to hear a Polk speaker that merits more than a sentence and 60 seconds discussion." :\
    My response is: If you need 60 seconds to respond in one sentence, you probably should't be evaluating Polk speakers.....


    "Green leaves reveal the heart spoken Khatru"- Jon Anderson

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  • tonybtonyb Posts: 31,123
    edited June 2014
    steveinaz wrote: »
    You guys give the phrase "wrapped around the axle" a whole new meaning. Stop "geeking" on go listen.

    I'll double up on Cathy's Amen to that.

    Sometimes this audio thing gets too wrapped up in such minor details, that the bigger audio gains are over looked in more obvious area's. Kinda like tripping over a dollar to pick up a nickel.
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  • FTGVFTGV Posts: 3,626
    edited June 2014
    steveinaz wrote: »
    You guys give the phrase "wrapped around the axle" a whole new meaning. Stop "geeking" on go listen.
    Its called Audio-nervosa,thats in part why some of us have multi thousands of posts on an audio forum.
  • SCompRacerSCompRacer Posts: 7,135
    edited June 2014
    FTGV wrote: »
    Its called Audio-nervosa,thats in part why some of us have multi thousands of posts on an audio forum.

    I think I've delved deep into digital enough to not want to discuss it anymore...lol
    Make yourself necessary to someone. Ralph Waldo Emerson

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  • FTGVFTGV Posts: 3,626
    edited June 2014
    SCompRacer wrote: »
    I think I've delved deep into digital enough to not want to discuss it anymore...lol
    Same.As well my ADD is progressing to the point that if a post is longer than 3 sentences,I move on.:)
  • SCompRacerSCompRacer Posts: 7,135
    edited June 2014
    FTGV wrote: »
    Same.As well my ADD is progressing to the point that if a post is longer than 3 sentences,I move on.:)

    I've been trying to improve my ADD, can you point me to anything that might help? :cheesygrin:
    Make yourself necessary to someone. Ralph Waldo Emerson

    Salk SoundScape 8's * Audio Research Reference 3 * Bottlehead Eros Phono * Park's Audio Budgie SUT * Krell KSA-250 * Harmonic Technology Pro 9+ & Pro 11+ * Signature Series Sonore Music Server w/Deux PS* Twisted Pear Buffalo III Dual Mono ESS Sabre32 DAC * Heavy Plinth Lenco L75 Idler Drive * AA MG-1 Linear Air Bearing Arm * AT33PTG/II & Denon 103R * Richard Gray 600S * NHT B-12d subs * GIK Acoustic Treatments * Sennheiser HD650 *

  • FTGVFTGV Posts: 3,626
    edited June 2014
    I find cable threads do wonders.With practice you should eventually find yourself tapping out after only 2 or 3 posts.
  • BlueFoxBlueFox Posts: 11,488
    edited June 2014
    FTGV wrote: »
    Same.As well my ADD is progressing to the point that if a post is longer than 3 sentences,I move on.:)

    Analog->Digital->Digital :smile:
    Bud - Silicon Valley

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  • OleBootOleBoot Posts: 490
    edited June 2014
    Uµtú…Å´Š™º6e“©ï'äÌØzKºVT¼ß\cEà…Úép’â1[µl³ðÆ„(PdÓkœÏ–Õi%+y¡‚f®Ä¯vŠ‰×ž%Ë+ä È€†ˆ!›Œ H}ȱ‡ûŒÞ·î¡á‹Ü—Hš.Újjµh8Øqø)¡Ô¡??^–¿ß’Ì‚¯XL’˜:½Ž;_ɐ6 ¤†™ð?ǧ.©ÈŠ9’Žº¢¡'(~|`ôÁ(’.5±ccèiŸ‰GÚb3.@¤“;±«Å’ï<nÆáÍ/†MÖ\¶J¼ºH2?ŠŽ’’I*“±|cʸ¬#i;$˜jÇÒhdΗ6 Ã>]z*9ñ-ãE[?ü¼°Ø¡¿²‹Ý)'ZðùIyø/|G˜ðŸ¢W‡)¶±R8(@j6&;Šé"´ïsÒ£Â@€;Ì
  • FTGVFTGV Posts: 3,626
    edited June 2014
    BlueFox wrote: »
    Analog->Digital->Digital :smile:
    LOL
    OleBoot wrote: »
    Uµtú…Å´Š™º6e“©ï'äÌØzKºVT¼ß\cEà…Úép’â1[µl³ðÆ„(PdÓkœÏ–Õi%+y¡‚f®Ä¯vŠ‰×ž%Ë+ä È€†ˆ!›Œ H}ȱ‡ûŒÞ·î¡á‹Ü—Hš.Újjµh8Øqø)¡Ô¡??^–¿ß’Ì‚¯XL’˜:½Ž;_ɐ6 ¤†™ð?ǧ.©ÈŠ9’Žº¢¡'(~|`ôÁ(’.5±ccèiŸ‰GÚb3.@¤“;±«Å’ï<nÆáÍ/†MÖ\¶J¼ºH2?ŠŽ’’I*“±|cʸ¬#i;$˜jÇÒhdΗ6 Ã>]z*9ñ-ãE[?ü¼°Ø¡¿²‹Ý)'ZðùIyø/|G˜ðŸ¢W‡)¶±R8(@j6&;Šé"´ïsÒ£Â@€;Ì
    Well said.
  • nooshinjohnnooshinjohn Posts: 20,817
    edited June 2014
    1110010001000 0100010 10100010 0001111 01 01001000 1011111 00101 001 1110001001000111.
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  • OleBootOleBoot Posts: 490
    edited June 2014
    1110010001000 0100010 10100010 0001111 01 01001000 1011111 00101 001 1110001001000111.


    I think your bits got affected by voltage pulses. The CIA do this, and it's not pleasant.
  • villianvillian Posts: 412
    edited June 2014
    BlueFox wrote: »
    Yes, perfect 1:1 digital copies are possible. In fact, it is more than possible. It is the norm. Of course, the potential for errors is there, but the technology has matured to the point where it would take a stray neutrino to create an error.

    Consider me surprised..
    Too many good quotes to list..waiting for some fresh ammo. :)
  • Habanero MonkHabanero Monk Posts: 716
    edited June 2014
    Now here is food for thought:

    http://www.rdm.com/en/Portaldata/1/Resources/International_PDF-Files_Library/White_Papers/english/STP-UTP_-_White_Paper.pdf

    Older 10/100 signaling methods are obviously slower but also less prone to outside interference. So people may want to consider only using 100Mbit and shielded CAT5/6. Since the cost is negligible and we know by Kurts testing CAT5 cables generally will past testing. Also assuming CAT6 ran at 100MB would be the optimal setup. Just force the NIC to 100MB signaling.
    So hot it burns twice :eek:
  • villianvillian Posts: 412
    edited June 2014
    headrott wrote: »
    My answer (which includes a rhetorical question) is: at what resolution are you analyzing and determining a "perfect" 1:1 digitally copied file when transferred? As was demonstrated by Ray's example in the "other" thread that the voltage pulses that correspond to a "1" or a "0" or a "high" or "low" can be transmitted and analyzed digitally as a "perfect 1:1" copy of the original source, but in fact the voltages are not the same as the orginal source material. They may be slightly higher or lower than the original material ("data source").

    These alterations to the voltage pulses are caused by different types of introduced noise (Electrical fast transient noise being an example). Also, things such as materials that these electronic pulses are transferred through can cause alterations to these voltages. Remember how much different PCOCC looks compared to TPC (Tough pitch copper)? As far as the computer is concered, the analyzed data pulses (despite being higher or lower than the original voltages sent through the cable and other parts of electronic equipment) appear to be "perfect" since as far as the computer is concerned they are either a "1" or a "0". When in fact, they are actually (to a greater or lesser degree) altered voltage pulses making up those "1's" and "0's" or "high" and "low" states.

    A person can listen with their ears and potentially determine that the altered voltages are in fact, not "perfect 1:1" digital copies of the original material while the computer simply sees the altered voltages and still demarks them as a "1" or a "0" making them apppear to be "perfect". Again, there is absolutely no perfect transfer of energy using the technology we possess; there is always loss to a greater or lesser degree. Always.

    So, no to your question villian and yes to your question Habanero Monk.

    Edit: I should specify in the answer to Habanero Monk's question that what the computer considers "bit perfect 1:1" files are possible because the computer still considers them a "perfect" "1" or "0". But the voltage pulses used to create those "1's" and "0's" were not perfect. So the answer is still yes to a person listening to the copied material (depending on the variation the voltage pulses of course). Once there is enough variation in the voltage pulses, the differences become much more obvious to a listen but still appear to be "perfect" 1's and 0's by the computer.

    I should also specify that it is these variations in voltages pulses that make up the noise in digitally copied material and also are what make up what is heard by the listener ( a less than perfect source).

    And Steve, I listen just as much as I go on a "geeking" spree. :smile:

    On some levels you're absolutely correct..as voltage changes do occur, and yes, the computer still interprets them as a zero or a one. That said, you are wrong about the voltage variations impacting the final reproduced file's sound. A zero and a one sound the same no matter what amplitude they are created at. In an analog world the variations would make all the difference, but in a digital world they are null and void. The logical output of a bit stream is the same as the logical input, regardless of external factors like voltage variation. The computer simply ignores the voltage variations because it can't even see them. Your DAC or any other digital component only see 1's and 0's. Nothing else can influence the processing of information that is received. If the voltage variations were so wildly different as to cause an audible distortion, then the file would be corrupted and unplayable. You're either going to get the full digital signal in all it's intended glory, or you'll get massive drops of data with blank spots of audio...if it's even playable at that stage. If the file is received as a 1:1 copy, there will be no difference in sound from the original.
    Too many good quotes to list..waiting for some fresh ammo. :)
  • headrottheadrott Posts: 5,428
    edited June 2014
    villian wrote: »
    On some levels you're absolutely correct..as voltage changes do occur, and yes, the computer still interprets them as a zero or a one. That said, you are wrong about the voltage variations impacting the final reproduced file's sound. A zero and a one sound the same no matter what amplitude they are created at. In an analog world the variations would make all the difference, but in a digital world they are null and void. The logical output of a bit stream is the same as the logical input, regardless of external factors like voltage variation. The computer simply ignores the voltage variations because it can't even see them. Your DAC or any other digital component only see 1's and 0's. Nothing else can influence the processing of information that is received. If the voltage variations were so wildly different as to cause an audible distortion, then the file would be corrupted and unplayable. You're either going to get the full digital signal in all it's intended glory, or you'll get massive drops of data with blank spots of audio...if it's even playable at that stage. If the file is received as a 1:1 copy, there will be no difference in sound from the original.

    So, you agree that there is no "perfect" copy of a digital file. Great! Something that is imprfect (voltage pulses sent through cables) do not "magically" become "perfect" when they become 1's and 0's (bits). That is in fact an impossibility. Nothing imperfect can create someing perfect. Now, you can try and rationalize the situation by stating that the computer, etc. attempts to make up for the lack of exact voltage pulses to create these "perfect" 1's and 0's (bits). I will then tell you that this would induce more noise to the signal, thus still making the copy imperfect. There are no perfect transfer of electrical signals, ever, period. How will you attempt to get around this logic? It cannot be done.

    I will then (based upon my reasoning above, and me listening to these imprfect digital transfers), go on to tell you that these imperfect transfer of elctrical digtal signals can be heard, just as analog signals can be heard. The transfer of digital signals are much more efficient (resulting in much less degredation of the signal) than analog signals, making the analog degredation much easier to hear, while the digital degredation is much lower and much more difficult to hear, but it can be heard when enough degredation is found in the digital transfer and the listener has high resolution audio equipment and has enough training to listen for the degredation of the digital signal.
    Relayer-Big-O-Poster.jpg
    Taken from a recent Audioholics reply regarding "Club Polk" and Polk speakers:
    "I'm yet to hear a Polk speaker that merits more than a sentence and 60 seconds discussion." :\
    My response is: If you need 60 seconds to respond in one sentence, you probably should't be evaluating Polk speakers.....


    "Green leaves reveal the heart spoken Khatru"- Jon Anderson

    "Have A Little Faith! And Everything You'll Face, Will Jump From Out Right On Into Place! Yeah! Take A Little Time! And Everything You'll Find, Will Move From Gloom Right On Into Shine!"- Arthur Lee
  • F1nutF1nut Posts: 42,130
    edited June 2014
    I voted no simply because the OP is a common troll and I'll never agree with a damn thing it says.
    Political Correctness'.........defined

    "A doctrine fostered by a delusional, illogical minority and rabidly promoted by an unscrupulous mainstream media, which holds forth the proposition that it is entirely possible to pick up a t-u-r-d by the clean end."


  • Habanero MonkHabanero Monk Posts: 716
    edited June 2014
    headrott wrote: »
    So, you agree that there is no "perfect" copy of a digital file. Great! Something that is imprfect (voltage pulses sent through cables) do not "magically" become "perfect" when they become 1's and 0's (bits). That is in fact an impossibility. Nothing imperfect can create someing perfect. Now, you can try and rationalize the situation by stating that the computer, etc. attempts to make up for the lack of exact voltage pulses to create these "perfect" 1's and 0's (bits). I will then tell you that this would induce more noise to the signal, thus still making the copy imperfect. There are no perfect transfer of electrical signals, ever, period. How will you attempt to get around this logic? It cannot be done.

    I will then (based upon my reasoning above, and me listening to these imprfect digital transfers), go on to tell you that these imperfect transfer of elctrical digtal signals can be heard, just as analog signals can be heard. The transfer of digital signals are much more efficient (resulting in much less degredation of the signal) than analog signals, making the analog degredation much easier to hear, while the digital degredation is much lower and much more difficult to hear, but it can be heard when enough degredation is found in the digital transfer and the listener has high resolution audio equipment and has enough training to listen for the degredation of the digital signal.

    I've posted a few technical papers on Ethernet signalling (MLT-3, PAM 5, PAM 16) I think when you read those you will come away with a better understanding.

    RAID 5 is another example of how you can have data split up into thirds/fourths/fifths etc and lose 1/3, 1/4, 1/5 and still you have all your data. XOR to the rescue in this case. You will still end up with a bit perfect file.

    I also posted two files and all you have to do is take 5-10 minutes to install the checksum (MD5 hash) and run it against the PDF and post the hash and we can compare. It doesn't matter if a variance in the signalling occurred. If the hash matches you have a 1:1 perfect file.

    Pretty easy and kinda cool in a geek only sort of way.
    So hot it burns twice :eek:
  • villianvillian Posts: 412
    edited June 2014
    headrott wrote: »
    So, you agree that there is no "perfect" copy of a digital file.

    Absolutely not.

    Where you pulled that from I do not know, as I've consistently stated that there are perfect copies of digital files. I agree'd with you that there are voltage variations in the signal used to transfer digital content. But, that voltage variation is needed to produce a digital file, and it in no way effects the reproduction of digital content..as the voltage simply signals a "Zero" or a "One"..regardless of it's amplitude.
    headrott wrote: »
    Something that is imprfect (voltage pulses sent through cables) do not "magically" become "perfect" when they become 1's and 0's (bits). That is in fact an impossibility. Nothing imperfect can create someing perfect.

    What you're failing to realize is that nobody is claiming that the voltage pulses are perfect, become perfect, or are a digital file in themselves. They are simply used to move digital content and signal how to reproduce the digital file. It doesn't take an "Exact" voltage pulse, it takes a pulse with a peak and a bottom (Which is nearly any pulse..). In laymans terms the variation between the two peaks doesn't matter. A peak *Represents* either a zero or a one, and the bottom of that peak represents the opposite. They are not literally the digital signal, they only convey it..and indirectly so. That is why a reproduced digital signal is the same as the one originally transmitted. When something doesn't go right and that signal is not recreated perfectly (For whichever reason), the receiving device simply requests the missing or deformed part of the file again..and it's resent until it is correctly reassembled. This can happen millions of times faster than real time, until a perfect, matching copy is created.
    Too many good quotes to list..waiting for some fresh ammo. :)
  • villianvillian Posts: 412
    edited June 2014
    F1nut wrote: »
    I voted no simply because the OP is a common troll and I'll never agree with a damn thing it says.

    Try again. Trolls don't waste their time posting to the Polk forum, going back and forth with a bunch of closed minded, self-proclaimed audiophiles. Not over simple ideas so trivial that my grandmother can understand them (As she does with digital reproduction..she plays a full game of solitare every single day), and espeically not in the vintage speaker sub-forum.
    Too many good quotes to list..waiting for some fresh ammo. :)
  • nooshinjohnnooshinjohn Posts: 20,817
    edited June 2014
    villian wrote: »
    Where you pulled that from I do not know, as I've consistently stated that there are perfect copies of digital files.


    If you already believe that, then other opinions are not needed as you have already closed your mind to anyone else's opinion but your own.
    villian wrote: »
    Try again. Trolls don't waste their time posting to the Polk forum, going back and forth with a bunch of closed minded, self-proclaimed audiophiles. Not over simple ideas so trivial that my grandmother can understand them (As she does with digital reproduction..she plays a full game of solitare every single day), and espeically not in the vintage speaker sub-forum.


    There you go, spoken like a true troll.
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    Saying that it's "too hard" to pursue your dreams is no different than admitting to yourself that you are too lazy to achieve them.

    “If it moves, tax it. If it keeps moving, regulate it. And if it stops moving, subsidize it.”
  • villianvillian Posts: 412
    edited June 2014
    If you already believe that, then other opinions are not needed as you have already closed your mind to anyone else's opinion but your own.

    I'm open to proof that I'm wrong, but nobody seems to be able to supply it. From what it seems like on here it's the minority making the most noise, as per usual. 24 people so far have voted in favor of perfect digital copies, and only 7 against it. My goal is to educate on the facts that I already know, nothing less and nothing more. That said, show me where I'm wrong and I'll gladly re-educate myself!

    I believe that Habanero has also challenged anyone to show or explain how bit perfect copies aren't possible..but nobody has stepped up??
    Too many good quotes to list..waiting for some fresh ammo. :)
  • nooshinjohnnooshinjohn Posts: 20,817
    edited June 2014
    villian wrote: »
    I'm open to proof that I'm wrong,
    No you are not. You made up your mind before your first post on the subject.
    villian wrote: »
    My goal is to educate on the facts that I already know, nothing less and nothing more. That said, show me where I'm wrong and I'll gladly re-educate myself!.

    When it comes to education, you get what you pay for. Considering your "education" cost me nothing, I guess you know what it's worth to me.
    The Gear... Carver "Statement" Mono-blocks, TriangleArt Reference SE with Pass Labs Xono Phono Preamp, Walker Precision Motor Drive, ClearAudio Goldfinger Diamond v2 cartridge and Origin Conquerer Mk3c tonearm, Polk Audio "Signature" Reference Series 1.2TL with complete mods, Pass Labs X0.2 three chassis preamp, PS Audio PerfectWave DAC MkII, Pioneer Elite SC-65, Oppo UDP-205 4K Blu-ray player, Sony XBR70x850B 4k, Polk audio AB700/800 "in-wall" surrounds.

    Saying that it's "too hard" to pursue your dreams is no different than admitting to yourself that you are too lazy to achieve them.

    “If it moves, tax it. If it keeps moving, regulate it. And if it stops moving, subsidize it.”
  • villianvillian Posts: 412
    edited June 2014
    No you are not. You made up your mind before your first post on the subject.

    And I'm willing to change it. Just give me a reason.

    Spouting off about voltage variation impacting a bitperfect copy of a digital file does nothing to help your side of the argument, as it's completely unrelated. It's like asking a car salesman to sell you on a sports car, and he walks you over to show you the cabin room of a 15 passenger van!
    Too many good quotes to list..waiting for some fresh ammo. :)
  • villianvillian Posts: 412
    edited June 2014
    Also, it should be noted that the title of this thread is "Are perfect 1:1 copies possible in the digital domain?"

    Not analog. Not in theory. In the digital domain.
    Too many good quotes to list..waiting for some fresh ammo. :)
  • ZLTFULZLTFUL Posts: 5,023
    edited June 2014
    "Some people find it easier to be conceited rather than correct."

    "Unwad those panties and have a good time man. We're all here to help each other, no matter how it might appear." DSkip
  • Habanero MonkHabanero Monk Posts: 716
    edited June 2014
    ZLTFUL wrote: »

    Good article and it trends with what I know:

    Hard disk systems are better in this respect, simply because it is in the nature of computers to copy data all the time. Consider the computer systems used by a bank. If there were any errors in the data, then concealment would be tantamount to fraud!

    Generally, when all is working well, a disk copy will be 100% identical to the original. This is thanks to the more robust error correction system used, and the 'verification' process where data is checked to be correct immediately after recording.

    Even so, glitches do happen, and the original recording should be kept safe just in case.


    I wonder how much studios still depend on tape based recording and mixing vs DAW/NLE?
    So hot it burns twice :eek:
  • pitdogg2pitdogg2 Posts: 13,753
    edited June 2014
    villian wrote: »

    Spouting off about voltage variation impacting a bitperfect copy of a digital file does nothing to help your side of the argument, as it's completely unrelated.

    No not really it's not^^^^^ Seems to me I was reading about a new CD player that cost north of 3-4g's. If the dac or whatever interprets that little loss of voltage as 180* opposite of what it should be then it is not bit perfect. 1 becomes 0 zero becomes 1. That player rips the CD until it gets a bit perfect word to send out to the speakers it needed 2 perfect copies before it will output the signal. So until it see the same ones and zeros in the same position it is not considered to be perfect....

    http://www.parasound.com/pdfs/CD1Whitepaper.pdf
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