Tuesday, January 24, 2012

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.


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  2. Which do you believe is more significant -- bigger sample size or higher sampling rate? Please leave a comment.