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Sound-quality of Class-D Amplifiers
Less distortion than class AB ?

A main disadvantage of class B is crossover distortion as discussed extensively by Douglas Self in EWW.
In most high quality amplifiers this distortion is reduced by rising the bias current, making the amplifier operate in Class A at low power levels. This reduces the distortion at the zero-crossings but the problem is then shifted to a higher level where class B begins.
Another distortion mechanism of class B is supply line pollution, When we look at the supply current during a sinusoid output signal, it looks like a single phase rectified sine with higher harmonics generated at the sharp edges. At higher frequencies the PSU rejection ratio is poor resulting in highly non-linear modulation of the output-voltage. An power supply with zero output resistance at all audio frequencies will prevent this problem. In better Analog amplifiers the housings are filled with caps of 10,000 mF or more per channel to reduce the supply resistance. In class A operation there is no supply problem at all, except the huge energy account. The current drawn is only DC.

Distortion mechanisms in class D
In a class D amplifier the distortion mechanisms, are complete different. Crossover at zero-crossings like in AB amplifiers does not occur.
A similar but very complex distortion mechanism is caused by the dead time period between the switching periods of both transistors. When both output transistors are in off-state, the output voltage at the transistor-output is dependent of the momentary current in the filter-coil, which is non-linear dependent of the momentary output-level, creating a voltage drop when the output-current reaches a certain level.
By switching on the 2 transistors fast after each other, with a dead time of only nanoseconds, this distortion-mechanism is minimized. In the remaining dead-time, the momentary output voltage is determined by the charging of the parasitic output-capacities by the inductor-current. A large parasitic transistor-capacity will smoothen this error-voltage, reducing the distortion to only low harmonics.
This distortion gets measurable (-100dB) when the output-current is reaching the peak of the sawtooth-shape idle-current of the output-inductor. This current draws no almost power when the Q-factor of the output inductor is high. In our amplifier LPC1 this idle-current is 1/3 of the maximum output current (12 Amps) so the dead-time-distortion begins at 10 dB below maximum output. Using the high inductor-current for fast  charging the parasitic capacity will also reduce the switching losses by ZVS.
The dead time is accurately matched to the charging time of the parasitic output-capacitors for minimizing distortion and switching losses.

The supply line pollution has of a much more friendly behaviour. Looking at the current drawn from the supply lines, its waveform has a low-frequency component, which is the square of the output signal. With a sinusoid as output signal, and a certain linear output resistance in the supply, a signal with the double frequency will be added to the supply voltage. In a PWM output stage with no feedback the output-signal will be multiplied with this supply voltage. A sinusoid output signal will be modulated by its square and thus resulting in pure third harmonic distortion.
It can be easily calculated that an output stage without feedback driving a 4 Ohm load to 80% of the supply voltage (80V), (resulting in 128W) and powered by a poor supply with 0.1 Ohm will result in 1% D3 distortion. If the supply is only buffered with a capacitor of just 3300 mF and the output stage is fed back with a bandwidth-product of 100 kHz, this D3 is reduced to 0.005% (-86 dB) at all frequencies. However when the supply is only buffered with large caps, low-frequency signals can cause second order inter-modulation at higher frequencies which is much higher than this calculated D3.
In the LPC1, the supply-line inter-modulation is cancelled completely by a patented circuit, making the amplifier open-loop gain fully independent of supply-voltage, even at 20 kHz.

The perceptibility of THD
The main explanation for the better sound-quality in this class-D amplifier is that the calculated and measured non-linear distortion mechanisms all result in distortion-components which increase proportional with the sound level. The relatively high THD-number  of the LPC1 (0.003% or 90 dB at 1kHz, 400W) comprises most low (3rth and 5th) harmonics.
This distortion is masked by the non-linear distortion and compression of most ears and loudspeakers. In contrast, the harmonics caused by crossover in class AB do peak at low output levels, and have a wider spectrum, making the same THD-number much more audible.