improved the sound. He says that the original CD format was limited to 16 bits of sound because of costs. But many audiophiles reacted very negatively to the tinny, metalic quality to the music.

Heh. Lack of sufficient bits for digital sound results in a floor of uniformly-distributed white noise for complex signals such as music. If audiophiles really hear "tinny" or "metallic" sound in double-blind tests, it would more likely be due to the sampling rate. The 44kHz rate means that skimping on the lowpass filter will push the cutoff into the audible range, which means you lose some upper harmonics and get to hear any phase nonlinearity in the filter.

For this reason, the companies have developed 20 bit DAT recording tape and then come up with ways to "dither" this into 16 bits.

I am curious if anyone knows the details of these algorithms.

Round to 16 bits. The higher-precision recording format is good because it lets noise (e.g. from mixing up a quiet signal) chew off four bits before it gets on the CD. You can do a little better than rounding, but not much.

Also, his point suggests that flipping the least significant bit of 16 bit music may not be imperceptable to some ears.

It may well not be, particularly if you do it without regard to the piece's amplitude. That 6dB of hiss may be perceptible during pauses. A more subtle flaw is that the signal will have artificial statistical characteristics. Natural noise in recordings is typically Gaussian, not uniform noise covering exactly one bit. What this means is that if the LSB is total uncorrelated hash, the bit above will have some noise. Look at a quiet passage. If the LSB is noise city and the 14th is uniformly zero, somebody twiddled with the digital data. This is a more reasonable way of screening for this sort of steganography than hiring a bunch of audiophiles. One fix is to cover your nefarious LSB activities by first adding sufficient Gaussian noise. My intuition, however, is that any amount short of microwaving the CD will leave a little bit of correlation between the original and the noised lower bits. With sufficient data, I think you can burn through the Gaussian noise and get enough information to make a call on whether the LSB has been twiddled. And a CD is a lot of data.

-Peter Wayner

Eli ebrandt@jarthur.claremont.edu