Lipshitz, S.P., J. Vanderkooy and R.A. Wannamaker, "Minimally-Audible Noise-Shaping,"
*J. Audio Eng. Soc.*, vol. 39, 1991 Nov., pp. 836-852

## ABSTRACT

Normal quantization or requantization noise is white, but the ear's
sensitivity to low-level broad-band noise is not uniform with
frequency. By adopting a suitable weighting curve to represent
low-level noise audibility, one can design dithered requantizing noise
shapers to approximate the inverse of the audibility curve and hence
achieve the least audible noise penalty. If Fielder's modified
E-weighting curve is adopted as a model of the 15-phon audibility
curve, a reduction of 10.9 dB in perceived noise is possible by
the use of a simple second-order noise shaper. This result is already
within 0.6 dB of the theoretical minimum set by information theory,
and almost a 2-bit gain in apparent signal-to-noise ratio. Even
greater perceived noise reductions are possible if one adopts an
audibility weighting curve which more closely approximates the ear's
precipitous high-frequency rolloff, and incorporates a higher order
filter into the noise shaper's feedback loop. In fact, a 20-dB
apparent reduction in the requantizing noise is then possible with
filters of modest order, but the penalty is a significant increase
in the total noise power. These questions are explored and some
of the available options illustrated. Such noise shaping will soon
be advantageous in order to preserve on the 16-bit Compact Disc the
lower noise floor of an original 18- or 20-bit master recording.