This is part 2 of a series on PGGB technology.
At the start of digital audio in 1980, Sony and Philips considered clinical measurements of our hearing to guide product specifications. At that time, it was determined that we can reliably detect a loudness change of about 1dB and a frequency change of 3-4Hz. Hence, the CD player was released with an 80dB SNR and 16bit audio. This was considered plenty good enough then ...but the development of high resolution digital audio formats and better components and transducers now indicates that the ear is much more sensitive.
Today, it is widely accepted that the threshold of human hearing corresponds to air vibrations on the order of a tenth of an atomic diameter - about one billionth of atmospheric pressure. This incredible sensitivity is enhanced by an effective amplification of the sound signal by the outer and middle ear structures. And this explains why we can consciously (and subconsciously) discern lower noise/distortion and why PGGB can make a difference to even the best DACs.
PGGB signal reconstruction produces a ultra high resolution (floating-point) internal result that has to be converted to the resolution of the DAC. The conversion from floating point to fixed-point uses noise shaping. This preserves the reconstructed signal through a combination of random dispersion and dithering of the quantization noise to higher frequencies. PGGB uses a high order noise shaper at high precision for lower than 400dB noise at 24-bit output - essentially zero.
Consider the sine wave represented above. The energy (sound pressure) is proportional to the area under the curve. At a bit depth of 24-bits(± 8,388,608), a sampling rate of 16fS (768kHz) and say, a 1kHz tone, a change of one bit at fS changes this area by less than one-billionth.
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Δ = 1 / 2^(23) * 1000/768000 = 1.5 x 10^(-10)
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This means a 24-bit signal at 16fS is (probably) sufficient to resolve human hearing. Over a single sample, the extra information imparted by PGGB is materially audible and, in aggregate over many samples, PGGB noise shaping can convey the full resolution of the reconstructed signal. IMO, this explains the uncanny increase in transparency that users' hear.
The next installment of this series will discuss the importance of a DAC's linearity on this transparency.