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In our Hierarchical paper [2] section 2.3 Temporal Limits, we explain:

"For the audio distribution channel we can consider temporal resolution in two aspects: its ability to maintain separation between closely spaced events (and not blur them together) and its ability to maintain a precise unquantized time-base within and between channels. Low-pass filtering may ultimately impact the separation of nearby events ... while filters in the digitizing process, that are sharper in the frequency domain, may also bring uncertainty to the start, stop…

If we look back at the roots of sampled coding systems we encounter Shannon's elegant reconstruction theorem and Nyquist's theorem on channel capacity.[23][24]

A sampled signal can be unambiguously reconstructed if it contains no frequencies higher then Fs/2; it is completely determined by capturing its values at a series of points T = 1/Fs seconds apart and can be reconstructed with a perfect low-pass filter at Fs/2.

There are a number of problems with this conceptual framework for the human listener. First, strictly mathematical, a…

Figure 7 shows the end-to-end impulse response for a typical CD channel operating at 44.1kHz. In Figure 8 we see…

There is significant content above 20kHz in many types of music, as an analysis of high-rate recordings summarized in Figure 14 has revealed. One notable and common characteristic of musical instrument spectra is that the power declines, often significantly, with rising frequency.

Even though some musical instruments produce sounds above 20kHz [27] it does not necessarily follow that a transparent system needs to reproduce them;…

Figure 18 compares the coding space for a number of common transmission formats, including CD, and 96 and 192kHz at 24- and 32-bit depths; also shown is the noise-floor for DSD64.

To accommodate the coding capacity of 32-bit LPCM, the vertical scale of this graph is formidable. At the top, 120dB SPL is the threshold of pain; 0dB (the quietest we can perceive) is in the center. The noise-floor of the 32-bit channel is 120dB…

• a) Is MQA really lossless?

• b) MQA isn't lossless?

• c) MQA prevents us changing the signal before playback (eg, room correction or upsampling).

Answers: • a & b) This question often seems to assume that lossless is always best but in fact all "lossless" does is to take some bits and to reproduce those same bits at another time or place. It that's all you wanted to do, FLAC would be fine and there would be no need for MQA. The team behind MQA understand not only lossless compression but also lossless processing and data burying. [3…

Again, these were posted online:

• a) MQA "folds" the double- and quad-rate audio data into the lowest bits below the baseband musical content of the 48/24 FLAC container. The "folded" MQA signal is fit into a 48/24 FLAC container for further compression. Undecoded MQA is claimed to restore the full baseband audio signal, but only to a bit depth of 16 bits, or 48/16. After all there are only 24 bits of resolution in a 24-bit FLAC container.

• b) How in the world has MQA fooled so many people into thinking that they could "fold" the…

We refer to the process by which MQA reduces high sampling rate signals to Fs = 44.1kHz or 48kHz as 'music origami', after the Japanese art of paper folding. Figures 14 to 16 show how it works for a 192kHz source.

Although the process is depicted here in two dimensions, it is actually a three-dimensional construct.

The first 'fold' (Figure 21) reduces the transmission rate from 192kHz to 96kHz, and the second (Figure 22) from 96kHz to 48kHz. The folding process is not filtering and the inherent sample rate and bit-depth remain. In the transport,…

This question was posed by some online commentators. We are giving a precis because the question has the wrong frame of reference.

Questions:

• a) MQA has publicly stated that the resolution of the baseband will depend on the spectral content of the music being encoded/decoded.

• b) By referring to widely respected Caltech Professor James Boyk's landmark paper on the high-frequency content of various musical instruments, "There's Life Above 20 kiloHertz! A Survey of Musical Instrument Spectra to 102.4kHz", we can easily see that all musical…

In the majority of our communication so far we have described one variant of MQA, while at the same time pointing out that the concepts, bitstream and system is hierarchical. What do we mean by that?

In fact MQA is hierarchical in a number of ways:

• The number of channels can be scaled upwards from 2.

• For music sampled at rates of 2x or higher, the playback sample rate can be optimised hierarchically by determining the 'unfolding' to suit the platform.

• The transmission rate can be scaled to be 1x, 2x, 4x or 8x. We have concentrated our…