100% Fidelity is Possible as We Approach Infinity. Are We There Yet?

A back-of-a-napkin capture of the Riemann Integral. 

The first step in ephemeralizing your LPs is to record them digitally, creating permanent archival copies. This is a step you only have to take once for each of your titles, but if you do it right, once is enough.

Recall that an information-rich map is always better than a back-of-a-napkin drawing. Create rich 24-bit/96KHz copies of your source material for archiving. Why? Read on.

Because we know we can't capture infinity digitally, the recording process is to sample the original; that is, to take a reading of the original sound wave at regular intervals Δ_i. The question is, how do we design a sampling process that will produce an optimal copy? Many people will tell you that "optimal" is a completely subjective characterization—not so (not "completely").

While virtually any scientific debate can turn subjective when opinion and evidence clash, math is uniquely impervious to opinion. "a(b + c) = ab + ac. Politicize that, bi***es." (Randall Munroe)

Without a priori knowledge about the sound being recorded, it is impossible to know if it is being captured accurately. But there is a proxy calculation that we can examine objectively.

A sound wave is a function F(t) of pressure v. time. Once a sample F(t_i) is taken at time t_i, the recorded sound value remains constant for Δ_i seconds until the next sample can be taken. Any Calculus Hero will recognize that, as we are sampling a sound wave, we are simulatneously calculating the Riemann Integral (approximate area below the curve) for it. Dude.

The width Δ_i and height F(t_i) of a rectangle in the Riemann Integral determine the accuracy of the approximation. Both dimensions are under your control. Let's concentrate here on getting the proper width via high frequency sampling. Next time we'll look at getting the proper height by taking the best possible samples.

The Riemann Integral aproaches 100% accuracy as Δ_i → 0. Thus you get progressively better approximations the more samples you can take in a closed interval. That's not my opinion, that's not even consensus opinion. That's math.

Because sound sampling is a real-time process, the total number of samples is less important than the number of samples you can take per second. This is your sampling rate, expressed in samples/sec or Hertz (Hz). Riemann says, the higher your sampling rate, the more accurate your source recording.

So what is a good practical sampling rate? Common sampling rates are:

• 44.1 KHz – CD Audio (CDDA)
• 48 KHz – DVD Audio (DVD-A)
• 88.2 KHz – 2x CDDA Rate
• 96 KHz – 2x DVD-A Rate

96KHz make sense for several reasons. First and foremost, it's higher that the other candidate rates (more is better). Second, 96 KHz is a common sampling rate supported by a wide variety of computer sound interface devices, so it's likely you can find one at a price you're willing to pay. Finally, because sampling theory says you can capture any frequency f  by sampling at twice that frequency 2f, 96KHz sampling captures frequencies up to 48KHz, well into the range inaudible to humans and above the upper range limit of even audiophile-class speakers.

Therefore my first recommendation for creating numerically accurate digital copies of your LPs is to set the sampling rate to 96 KHz. What do you think? Leave a comment.

              Vinyl-to-Digital Restoration #10              

Title: Gallery

Artist: Gallery
Contributing Artists: David Samuels; Michael DiPasqua; Paul McCandless; David Darling; Ratzo Harris
Genre: Jazz
Year: 1982

Despite the personnel involved having a pretty damn good pedigree, this album is lost to history. ECM Records never released it on CD, and even today has no entry for it on the ECM discography. Long ago I bought Gallery on vinyl for its link between the Paul Winter Consort and Orgeon. One of the best reasons for shepherding your analog past into the digital future is that your memory can be jogged. The record labels' memory can't.

© 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.