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Letters: Digital and Analog Resolution, RH replies

Letters: Digital and Analog Resolution, RH replies

Analog and Digital Resolution

Some years back, in a review of the Benchmark AHB2 power amplifier, the reviewer opined that the differences between competently designed amplifiers had become so small that he thought that amplification was a “solved problem.” The editor of this magazine felt compelled to add a comment in parentheses right after this stating that this was not the opinion of the magazine. Were I him, I would have told you clearly what I thought of your comments in the middle of my article.

In issue 324 you have the always-analog JV stating that “analog tapes recorded at 15/30 ips are virtually infinite in resolution; they are continuous copies of a live event, without any of the myriad of tiny “gaps” (the little “bits” of missing information) of digital copies—the sound content of which must be filled in via the educated guesswork of your DAC.”

Where is the editorial comment? Analog tape does not have infinite resolution [Jonathan used the phrase “virtually infinite,” not “infinite.”—RH]. Not even close. Analog and digital recording produce different sorts of artifacts as they approach their resolution limits but neither has infinite resolution. This old saw frequently trotted out by analog addicts is nonsense and has always been nonsense. The resolving power of any record/playback system is revealed by the difference between the recorded signal and the playback. By any known measure, high-resolution digital PCM (even CD-resolution PCM) outperforms analog tape by a wide margin. How does worse dynamic range and 1000 percent more distortion equal better resolution? Believing in magic doesn’t make it real. I would have thought this statement deserved a parenthetical comment that it showed a profound misunderstanding of both analog and digital recording.  

– Bob Wortman

 

RH replies: Your assertion that “even CD-resolution PCM outperforms analog tape by a wide margin” is simply wrong, both on a technical level and experientially. The term “resolution” is grossly misunderstood in digital audio. Technically, resolution is the ability to distinguish between two closely spaced objects, events, or values. 

In the amplitude domain, digital audio has demonstrably lower resolution than analog tape because it has a finite number of quantization steps (65,536 for 16-bit PCM). When an analog value falls between two quantization steps, the quantizer assigns the closest value, even though the quantized value doesn’t precisely represent the analog signal’s amplitude at the sample point. Think of it as rounding error. In addition to this theoretical problem of quantization error, manufacturing tolerances mean that the steps between the discrete values are not perfectly uniform. This introduces even greater uncertainty in the digital representation of an analog waveform’s amplitude—lower resolution, in other words. 

Further, the resolution of a digital system isn’t defined by the number of quantization steps available (the aforementioned 65,536 steps for CD-quality audio), but by the number of steps being used at any given moment. A quiet musical passage may be encoded with only four bits, which can encode just 16 discrete amplitude levels. 

In the time domain, resolution is the ability of the system to distinguish between two events closely spaced in time. The time smearing and ringing introduced by digital filters, particularly those required for 44.1kHz sampling (smearing on the order of 5µs), makes it impossible to distinguish between two closely spaced sonic events—again, lower resolution.

Contrast the discrete nature of digital audio with the virtual continuousness of analog tape recording. First, analog tape doesn’t introduce the time-domain smearing of digital filters. Secondly, the needle-shaped magnetic particles on tape are 0.5 to 0.1µm in size (about 800 such particles equal the width of a human hair), and each particle can contain more than one magnetic “domain” that can be independently magnetized. Each inch of tape is coated with many tens or hundreds of millions of such particles. When viewed in this light, I think that Jonathan’s description of magnetic-tape resolution as “virtually infinite” is accurate. 

Open-reel analog tape has its shortcomings, but resolution, in the true sense of that word, is not one of them. 

Tags: ANALOG DIGITAL EDITOR LETTERS ROBERT HARLEY

By Robert Harley

My older brother Stephen introduced me to music when I was about 12 years old. Stephen was a prodigious musical talent (he went on to get a degree in Composition) who generously shared his records and passion for music with his little brother.

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