Sidebar: Resolution and Dynamic Range
When you add more bits to a digital format, you add more potential volume levels. A 16-bit system has 65,536 unique levels; a 24-bit system increases that 256 times, to 16,777,216 levels. It seems reasonable, then, to use the word resolution to describe what you gain when you add more bits.
Apparently, though, it isn't. Benchmark's John Siau told me in an e-mail exchange that if a digital system is properly dithered, those discrete levels don't really exist—and on further thought, it makes sense. "If the digital audio is TPDF dithered"—TPDF stands for Triangular Probability Density Function, the best kind of dither—"the bit depth determines the SNR of the digital channel but does not limit the 'resolution' or number of 'volume levels,'" Siau wrote. "It is precisely equivalent to adding random noise to the analog input. No distortion is added and no audio details are lost. Very-low-level musical details still exist and can be seen on a spectrum analyzer. These details may be masked by the noise, but this is exactly the same thing that would happen if the same amount of noise was added in the analog domain. When TPDF dither is properly applied, a piano decay will sound just like the original, but with added noise. The bit depth of a TPDF-dithered digital channel determines the channel SNR and nothing else."
In contrast, "if the digital audio is not dithered, the volume levels are quantized and small signals can disappear entirely. Larger signals will be distorted by the quantization. The distortion will be a combination of harmonic and intermodulation distortion. If dither is not used, a piano decay will sound distorted and will end abruptly." Essentially, all music recorded digitally, for at least 30 years, employs dither (footnote 1), either intentional or—for high-resolution recordings—naturally occurring in the form of thermal noise (footnote 2).
"I like to do 8-bit demonstrations where I play a 3kHz tone that is 30dB lower than the dither noise," Siau continued. "The SNR of an 8-bit TPDF system is only 45dB, but our ears can hear a 3kHz tone at –75dBFS in an 8-bit TPDF-dithered system. An FFT analysis shows that the –75dBFS tone is distortion-free."
Resolution, then, is not the right word for what you lose when you reduce the bit depth of a properly dithered audio signal. A much more apt term is dynamic range.—Jim Austin
Footnote 1: Early digital recordings weren't properly dithered, if at all. A notorious example is Ry Cooder's Bop Till You Drop, recorded on an early 3M machine and released in 1979 on LP.—John Atkinson
Footnote 2: Actually, as Stanley Lipshitz once demonstrated at an AES convention, analog thermal noise doesn't act as dither unless it is at the appropriate level. Higher than that level and it is just part of the analog signal to be digitized.—John Atkinson
Footnote 1: Early digital recordings weren't properly dithered, if at all. A notorious example is Ry Cooder's Bop Till You Drop, recorded on an early 3M machine and released in 1979 on LP.—John Atkinson
