All Bits are Significant; Some are More Significant Than Others

Neil Young told MTV News that listeners of MP3 audio hear only "5 percent" of the data in an original recording. He continued: "We're in the 21st century and we have the worst sound that we've ever had. It's worse than a 78 [rpm record]."

The math is solid. Looking at raw numbers, 24-bit/96KHz LPCM sound has 18x the bit rate of a 256K MP3. Invert that, and you get an MP3 worth roughly 5% of the original.

[Image credit: ~4ntigravity.]



But is bit rate alone a good relative measure? I'd like to convince you that it is not. Sample size is key.

In any discussion of bit rates, a chart like this is employed at some point. I'm guilty of using it myself. The trouble is, if you're trying to be more specific in making format comparisons than simply 'more is better,' reducing the argument to numeric multipliers is simplistic. All bits are significant; some are more significant than others.

Information increases exponentially with bit width.

Information is a measure of decrease in uncertainty. Saying that a sound sample can be encoded in N bits implies that N yes/no questions must be answered to resolve the uncertainty of its actual value. The maximal uncertainty to resolve (and hence potential information content) grows exponentially as sample size N increases.

As Carl Sagan said, not all bits have equal value. The greatest uncertainty is  removed by question 1, or the most significant bit (MSB), so this bit has the highest information value. The smallest uncertainty is removed by question N, or the least significant bit (LSB), so this bit has the lowest information value. Paradoxically, answering the questions becomes increasingly harder as you progress from MSB to LSB due to greater detail being supplied, i.e. the more sample bits you want, the more difficult they become to obtain.

In contrast, information content grows linearly with sampling rate. Doubling your rate produces twice as much information. Tripling the rate triples information, and so on.

Thus information contributed by sample size and sampling rate increase on different scales. While 24 16-bit samples and 16 24-bit samples have the same bit total, the larger samples took more effort to obtain and are more valuable bit-for-bit. I previously said you should seek and preserve maximum bits in the vinyl-to-digital transfer process. What I really meant was, seek and preserve information value.

Choose bigger samples over higher sampling rate if you can't maximize both.

              Vinyl-to-Digital Restoration #12              

Title: Live Rust
Artist: Neil Young & Crazy Horse
Genre: Rock
Year: 1979



Music buyers who only know an industry dominated by iTunes can't imagine a time when you needed to buy an entire double LP set just to get the one or two tracks you really wanted. The most significant bits for me on this title are from "Powderfinger" and "Like a Hurricane." Well worth the effort to obtain.

© 2012 Thomas G. Dennehy. All rights reserved.

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.