Dr. AIX's POSTS — 16 September 2014

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I’ve talked about digital sampling and the advantages of 24-bits over 16-bits here in the recent past. And there have been a few pointed comments regarding some of my assertions. I try to keep myself open to other points of few but when they run counter to my own knowledge and experience, I seek help from other knowledgeable individuals. As most of you know, one of the smartest and most experienced electrical engineer/digital system designers I know is John Siau from Benchmark Media. I wrote to him recently about some of the issues relating to word length etc and this was his response. He granted my request to post it. It’s an interesting read.

Wow, your reader is very confused! I don’t even know where to begin.

Has he read my application note [read it here] where I give the example of 1-bit DSD? If he hasn’t, it should give him some food for thought. By his accounting DSD should be capable of one or two levels and should be highly distorted. The fact that a 1-bit digital system can produce a high-quality recording debunks much of what he is claiming.

Many people get drawn into his train of thought because they envision DAC outputs as stepping from the quantization level at one sample to the quantization level at the next sample. This is known as a zero-order hold. This would generate a series of triangular-shaped error signals where one triangle occurs at each sample. These high-frequency errors can be removed with a brick wall analog lowpass filter with a cutoff frequency that is at or below the Nyquist frequency. But, no modern DAC actually works this way! All modern DACs are oversampled, and the spectrum of the error signal is well separated from the audio band. With this oversampling, virtually all of the error signal (due to sampling) is removed, and the input sample rate has no bearing on the amplitude of the error signal.

Each sample should be looked at as an impulse. Upsampling DACs insert 0-amplitude samples between each actual sample. An upsampling ratio of 256 inserts 255 0-value samples between each successive input sample. This series of impulses (most of which are 0) feed into a sin(x)/x reconstruction filter. The result is a high sample rate waveform containing the original signal plus some high frequency noise. A zero order hold is often unavoidable, but this typically occurs at 256Fs in an oversampled DAC. This implies that the noise produced by the zero-order hold starts near 256/2 * the original sample rate. This high-frequency noise is well above the Nyquist frequency of the original samples and is easily removed with a simple analog low-pass filter. The end result is a continuous band-limited waveform that is an exact replica of any band-limited input waveform. All of the remaining noise is a result of quantization errors and dither noise. If dither was properly applied before quantizing in the A/D, the errors will be random. The end result is the original continuous waveform plus white noise, where the white noise is not correlated with the audio.

All existing 24-bit A/D converters generate enough thermal noise to provide adequate dither for the initial conversion process. This thermal noise gives 24-bit A/D converters a linear response. This is not always the case with 16-bit A/D converters, or 16-bit outputs from 24-bit converters. These low-resolution converters often need to have dither added in order to achieve a linear amplitude response.

Any DSP operation the involves truncation will need an additional application of dither prior to the truncation.

The sin(x)/x filter reconstructs the original continuous band-limited signal from a series of uniformly spaced samples.

Your reader seems to have a general disregard for the Nyquist theorem. This leads to all sorts of erroneous conclusions. He seems to dismiss Nyquist as obsolete.

There is nothing obsolete about the Nyquist theorem, the physics and mathematics have not changed.

John Siau

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About Author

Dr. AIX

Mark Waldrep, aka Dr. AIX, has been producing and engineering music for over 40 years. He learned electronics as a teenager from his HAM radio father while learning to play the guitar. Mark received the first doctorate in music composition from UCLA in 1986 for a "binaural" electronic music composition. Other advanced degrees include an MS in computer science, an MFA/MA in music, BM in music and a BA in art. As an engineer and producer, Mark has worked on projects for the Rolling Stones, 311, Tool, KISS, Blink 182, Blues Traveler, Britney Spears, the San Francisco Symphony, The Dover Quartet, Willie Nelson, Paul Williams, The Allman Brothers, Bad Company and many more. Dr. Waldrep has been an innovator when it comes to multimedia and music. He created the first enhanced CDs in the 90s, the first DVD-Videos released in the U.S., the first web-connected DVD, the first DVD-Audio title, the first music Blu-ray disc and the first 3D Music Album. Additionally, he launched the first High Definition Music Download site in 2007 called iTrax.com. A frequency speaker at audio events, author of numerous articles, Dr. Waldrep is currently writing a book on the production and reproduction of high-end music called, "High-End Audio: A Practical Guide to Production and Playback". The book should be completed in the fall of 2013.

(4) Readers Comments

  1. Well I stumbled onto your website recently while searching for HD downloads. I’ve been downloading from HD Tracks for over a year with mixed satisfaction. First with a Mac Mini connected to a surround system in my home office driven by an NAD receiver. Couldn’t tell a bit of a difference frankly. But I knew the whole system was marginal for music. Then last year, my local high end audio store had a used SOTA turntable on consignment. I went to look at it and left with it, a new Audio Research SP17 preamp and a set of Golden Ear Triton 2 speakers. Then picked up an almost new Audio Research VS60 amp. Wired it up with Nordost. Powered it up with Shunyata. Bought a Halide DAC for the Mac and began to listen again. Huge difference between some HD downloads and the original CDs. So much so that I realized the weakness with the old lame SOTA table. Upgraded recently to a VPI Classic1 and swapped the Halide for the new Rotel DAC. Now I can finally hear most if not all the differences. Started reading your posts and understanding your basic premise regarding provenance (you are so right) but more importantly your fundamental belief that high res recording is better than analog recording. It was taking me a little while to accept this since most vinyl just sounds better than most digital. Then today, I remembered an experience I had a very long time ago. 1980 to be exact. I was living in Atlanta and visited Jim Smith’s store in Birmingham a number of times trying to decide whether or not to buy a Linn table. On one of these visits he played his HQD (I think thats the right acronym) system of stacked Quads, Hartley sub?, Decca tweeter? driven by early “real” Mark Levinson electronics. The source? A digital master tape that he had personally recorded of the Atlanta boys choir. I had never heard nor since have heard that level of realism. It was truly like being there. And the most freaky thing was that the entire orchestra was coming out of the floor. Or orchestra pit in reality. The imaging was out of this world. The reality was awe inspiring. Until reading your posts, I had forgotten the best audio experience of my life. All this to say that YOU ARE ABSOLUTELY RIGHT!

    • Thank you and welcome to RealHD-Audio.com.

  2. It would’ve really helped if you had told us what the reader had said that led to this post. What was the reader’s misconception? You say it was “issues related to word length,” but what specifically?

    • I’ll see what I can do. You’re right, of course. But I want to respect the privacy of the original reader and thus thought it best to withhold his exact comments.

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