Is digital pure?

September 24, 2022
 by Paul McGowan

13 comments on “Is digital pure?”

  1. Reconstruction of a sine-wave based on only two sample-point is only possible because the “algorithm” was told to construct a sine-wave! Neither a square-wave, nor a saw-tooth wave etc! However music is characterized by more or less steep transients being only captured and reproduced when using DSD as you mentioned, Paul, for those delicate sounds as brush strokes on a cymbal or plucked strings of a guitar or cembalo. Thus shouldn’t the question be when digitizing via PCM which sine-frequency has the same rise-time as the sharpest transient being captured by a microphone which already is dampening the incoming signal due to mechanical and electrical inertia-effects? I am pretty sure it needs a sine-frequency far higher than 192 kHz to get the sharpest transients for plucked string instruments or percussions.

          1. FR, my “??????” rather referred to the obvious misunderstanding of my comment which focuses on the non-realistic simplifications and assumptions of the reconstruction-schemes. It would be most interesting get to know why DSD64 requires at least a sampling frequency of 64x44.1 kHz (why not DSD32 or DSD50) and why 24/705.6 or 24/1411.2 wouldn’t do it even better for recording?

    1. I once read an article comparing the pulse response of DSD vs PCM.The single rate DSD reproduced a perfect replica of the original analogue pulse whereas 44k PCM only managed a pulse heighth half of the original with noticable pre and post ringing.88k PCM managed two thirds the pulse heighth with half the ringing of 44k.176k PCM managed three quarters of the pulse heighth with half the ringing of 88k.
      A 10khz squarewave was reproduced perfectly by DSD whereas the best that 44k PCM could do was a sinewave!
      I think this proves the superior transient performance of DSD over PCM.

      1. And maybe DSD128 is required for a 20 kHz square-wave? 🙂 Wouldn’t it be interesting to see the same measurements for analog master tapes and vinyl records? Isn’t it revealing that Michael Fremer’s digital PCM-recordings of his vinyl records should already fully capture sonic differences of the quality of different cartridges? 🙂 There even is a DAC out there which emulates the “sound” of vinyl records: “Vinyl Emulation - get that special sonic character of a record player based playback chain. We also employ an emulation of the DMM-CD procedure offered by the Stockfisch label.” . See: https://www.weiss.ch/products/dac501-dac502 Thus again my question: What is the minimum sampling frequency for fully (!) capturing the audible (!) cues of music/characteristics of sharp transients?

    2. Re "Reconstruction of a sine-wave based on only two sample-point[s] is only possible because the “algorithm” was told to construct a sine-wave!": For this particular process step, I don't believe that any wave-shaping algorithm instructions ("telling") is involved. I believe it is simply the result of passing reconstructed samples from the 20 kHz bandwidth-limited input signal through the similar 20 kHz output low-pass filter. For example, a Red Book CD 20 kHz sine wave signal (even if only one cycle) will have even the 2nd harmonic (40 kHz - a totally inaudible frequency regardless of its amplitude) totally filtered out (-90 dB or so), yielding a 20 kHz sine wave output. Lower-frequency signals with more complex waveforms will have more samples present, which will result in a nicely reconstructed waveform. E.g., a 1 kHz square wave will have 44 samples for each cycle and will be reconstructed rather identically to the necessarily-by-design 20 kHz bandwidth-limited input signal. All of the "missing" higher-order harmonics will be above 20 kHz and therefore inaudible in both the filtered input and output signals. The same concept applies for all audible frequencies of the bandwidth-limited input signal up to around 20 kHz, including any type of complex music signal. Any higher sampling rates (e.g., 48 kHz, 192 kHz) would allow the input and output of higher frequencies, but they would be ultrasonic and therefore inaudible. Some people can hear subtle differences between filters with different high-pass cutoff points and different slopes, so such higher sampling rates can permit the use of filters with higher cutoff points and/or lower slopes, with resultant subtly higher flat frequency response and/or less high-frequency phase distortion, for the benefit of those who can hear it, but of course at the expense of more memory to store (or bandwidth to transmit) such digital signals.

  2. Paul I'm nit-picking but CD is a specification not a standard.
    The stair-step factor is utter bilge water promoted by dodgy diagrams that have confused folk for years now. PCM captures points of reference - the question troubling folk is what about the gaps between those points of reference (sampling)? At 192/24 or above there is nothing to be concerned about regarding frequency, dynamic range or timing and as you have discussed it allows more gentle filters to reconstruct the signal. However in PCM vs DSD, PCM appears to lose some quality in overall sonic delivery hence the continuing championing of DSD by many very reputable recording engineers.

  3. Ok, perhaps I could be missing something here.
    But I heard Paul on many au cations, say that all of the power plant regenerators constructs the outputs using DSD.
    But he never told us all both how and why.
    If I'm wrong, then someone on here please correct me!

  4. Paul, THANK YOU so much for this post! So many people only know enough about digital audio to "be dangerous". They've seen many stairstep signal representations of just the sampling and quantization processes, and therefore have a fundamental misunderstanding about what's happening in the signal processing and a never-ending bias about the supposed "evils" of digital audio (such as significant "missing" signal information). This article SHOULD help them overcome that misunderstanding and bias. However, those mistaken beliefs are so deeply rooted, I'm not holding my breath - many examples are there in the comments from people who presumably listened to the entire video. Most (not all, but MOST) of the differences that I have heard between analog tape or LP vs CD or better digital copies of the same recordings are a result of (1) the different sources used (e.g., 1st generation multi-track tapes vs other copies), (2) mix variations (e.g., amplitude, equalization, compression, echo/reverb, etc.), and (3) the inherent noise/distortion characteristics of the analog media (e.g., tape hiss, dirty tape heads, 2-dimensional tape head misalignment, dirty styli or record grooves, 3-dimensional phono stylus misalignment, dynamic stylus mis-tracking, different stylus shape geometries, vinyl pops/ticks, etc.). When I started building my CD collection in my early 30s (with good hearing up to 20 kHz or beyond, and listening to a variety of audiophile-grade CDs & equipment including different turntables, tone arms & cartridges, tube and solid-state electronics, and electrostatic speakers & headphones), I did indeed find CDs that sounded significantly inferior to my old best LPs and tapes - but it was almost always due to obviously different equalization used in the media mastering processes or different source tapes that were mixed or otherwise mastered differently. The plethora of additional signal processing techniques that were developed since then (e.g., dynamic noise filtering software) add to the possible variation reasons, but in my judgment, equalization and compression differences remain the worst and most obvious offenders. I trusted my younger excellent hearing, not the "digititis" phobias believed by and promulgated by others. [BTW, younger readers might be interested to learn that typical moderate amounts of age-related hearing loss above, say, 7 kHz has almost no impact on music enjoyment and instrument discernment. For music, the top octave or more of highest-possible human hearing consists almost entirely of rather low-level harmonics (not fundamental frequencies), which have little effect on discerning the upper-register sounds of different instruments playing the same notes or range of percussion sounds. E.g., the inability to hear the 16 kHz sine wave in the side 2 runout groove of The Beatles' Sgt. Pepper album doesn't necessarily mean that even instruments like cymbals, jingle bells, tambourines, etc. can't be distinguished, although more profound amounts of hearing loss can of course make an extreme difference.]

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