We'll Always Have Paris. Or a 24-bit Approximation of Paris.

Quantization maps infinite sets of real values to single values.

When it comes to digitally recording music from analog source material (LP, tape) the best approach is, "Sample often, sample well."

In a previous post we introduced non-subjective numerical methods to establish 96 KHz (ninety-six thousand samples per second) as an information-rich practical sampling rate. That takes care of "sampling often."

But what about "sampling well?" Can near 100% accuracy be achieved for the samples being collected? 24-bit word size is the closest practical approximation. Why? Read on.

Digital sound samples are real numbers in the closed interval [-1, +1] and can take on any of an uncountably infinite number of values within that interval. The sound capture process therefore must quantize the infinite set of real sample values into a set of approximating values that has a finite size yet is still information-rich. How big should that set be and how many bits are needed to represent its members?

With b bits available, a value set of size 2^b (2 raised to the power of b) can be encoded. At one bit, the sign bit, there are two values available (2^1 = 2) and we can only express whether a sample is greater than 0 or less than 0. Arbitrarily assign the value +0.5 to any positive sample (bit value 0) and -0.5 to any negative sample (bit value 1). The maximum quantization error ε with one bit is 50% (± 0.5). Clearly we need more bits.

Each bit added to the sample word doubles the size of the quantized value set it can represent and cuts quantization error by half. There is a well-known term for this—exponential growth. Not only does the sample set expand as you add bits, the rate of that expansion accelerates.

At 8 bits, 256 values can be represented and ε is just under 0.5%. Not good. At 16 bits, the set has more than 65,000 values and ε around 0.002%. Better, but still room for improvement. At 24 bits, the set has more than 16 million values and ε around 0.000006%. Every added bit is more significant than all the bits that came before it, up to a point. When does adding bits stop adding information?

A copy can't contain more information than the original. Most digital studio recording is done at 24-bit, so adding bits beyond that in the home audio capture process adds no new information on digital-to-analog source material (e.g. new releases on vinyl). Using 24-bit sampling to record analog-to-analog material (old vinyl) mimics current industry best practices. And 24-bit is a sample size supported by more and more computer sound interface devices, so it's likely you can find one at a price you're willing to pay.

Therefore my next recommendation for creating numerically accurate digital copies of your LPs is to set the sample size to 24-bit when recording. What do you think? Leave a comment.

              Vinyl-to-Digital Restoration #11              

Title: Waiting For Columbus

Artist: Little Feat
Genre: Rock
Year: 1978

Double albums present special challenges in the digital transfer process. Live albums present still other challenges. Double live albums are a double whammy. If a multi-disc set comprises a single work, you must normalize the output sound level across the entire set (not disc by disc) to prevent odd changes in volume if you shuffle the tracks. Deciding exactly where to split between tracks on a live album (during applause) is an art, not a science. You'll be happy to have a 24-bit/96KHz recording on which you can zoom way in to make a precise cut.

© 2012 Thomas G. Dennehy. All rights reserved.

LPs and CDs Are Fraternal Twins

An LP and his digital twin.

Raise your hand if you think there are files on a CDDA disc (an "audio CD").

OK, put them down. There is some misinformation out there.

When you put an audio CD into your computer's drive, Windows Explorer will display a CDA (CD Audio Track) file for each track. If you double-click one, Windows Media Player opens and plays the track.

But the files don't really exist. Each one is a shortcut to where the corresponding audio track starts on disc. Explorer just calls them files because files are what it understands. Without the physical CD loaded, the "files" are meaningless.

A CD is a continuous laser groove of 16-bit digital stereo audio samples, starting at the inner edge and radiating outward. The implicit sampling rate is 44.1 KHz, meaning no time information needs to be encoded with the audio.

An LP is a continuous physical groove capturing an analog stereo waveform, starting at the outer edge and radiating inward. The implicit recording and playback rate is 33 1/3 rpm.

Both are round, have a hole in the center, spin while playing, and are read by a tracking sensor.

Thus, they are fraternal twins. A CD is basically a digital LP (played in reverse, but not saying Paul is dead). That's one reason CDs and LPs share common playback inconveniences, and why dematerialized digital playback has made the CD seem just as clunky as his analog twin.

In my professional life at Harman International, I manage development of multimedia infotainment/navigation systems for the OEM automotive market. Our newest systems don't even include a CD player. An iPod/USB interface is now standard, reflecting the market preference for dematerialized play.

But that didn't stop an OEM customer's test group from flagging a Harman system because "it didn't play CDA files." They thought that dragging and dropping CDA files onto a memory stick was equivalent to making an audio copy of a CD. We quietly buried the bug report as "not reproducible" (so to speak).

Our digital transfer process for LPs will produce more accurate results.

                Vinyl-to-Digital Restoration #1              

Title: The Survivors' Suite
Artist: Keith Jarrett
Contributing Artists: Charlie Haden, Dewey Redman (1931-2006), Paul Motian (1931-2011)
Genre: Jazz
Year: 1976

My interest in jazz got its start with a college housemate's copy of Keith Jarrett's The Köln Concert. But it really took off in grad school as I started mining through the ECM catalog at dear, departed Schoolkids Records in Ann Arbor MI. My jazz holdings stand now at roughly 250 titles, and you can trace a path back from virtually any of them to one of the four members of this quartet.

The most labor-intensive task in the digital transfer pipeline is extracting and isolating individual LP tracks. Not surprisingly, the task time grows linearly with the number of tracks on the disc. You're grateful for a title like The Survivors' Suite, where side 1 is track 1 and side 2 is track 2. Quick and clean.



© 2011 Thomas G. Dennehy. All rights reserved.