Please pardon the below shameless product design mugging; I promise that it will clear up closed form math questions. Incorporated in the Yggy and also in the new multibit Gungnir - The Schiit Footlong Mega Combo Burrito Digital Filter:
It is a digital filter/sample rate converter designed to convert all audio to 352.8 or 396KHz sample rates so that it may drive our DACs. You get it uniquely from us; it is our filter. It took five people many years to design and perfect at the dawn of digital playback, way back in the early eighties. It keeps all original samples; those samples contain frequency and phase information which can be optimized not only in the time domain but in the frequency domain. We do precisely this; the mechanic is we add 7 new optimized samples between the original ones.
All digital filters multiply the original audio signal by a series of coefficients which are calculated by a digital filter generator. Over the years, before Theta Digital was born (my original company), we developed this filter design/generator. The common digital filter method is a Parks-McClellan algorithm, which has been used in all of the older oversampling chipsets, and persists to this day as the input filter in most ds DACs. Why? I assume it is because it is royalty-free, and the algorithm is widely available as are digital filter software design packages to aid in a cookbook aproach to the design. Now Parks McClellan an open form math solution, which means that the coefficient calculation is a series of approximations which always get halfway there. This of course, means it never completely solves. The worse news is that all original sample are lost, replaced by 8 new approximated ones. Further, the Parks McClellan optimization is based on the frequency domain only flat frequency response, with the time (read spatial) domain ignored.
Our filter is based upon closed form math the coefficients are not approximations, the equations solve; the matrices invert and the math is done. The filter also optimizes the time domain.
This is the reason that on good recordings (with good playback system as well) through Yggy (and now Gungnir multibit) you can hear the hall, its dimensions, and the exact position of anyone coughing or farting in the room, the motions and locations of instruments being hoisted in preparation of being played, etc. etc. Details such as sheet music pages being turned are not muddled because of clear differential spatial cues. This comes exclusively from our filter. A friend of mine, Jonathan Horwich, sells master tapes in track form at least 15 IPS, and 30 (I believe) as well. On those analog masters, you can also hear the entire environment before the music starts what is amazing there is that even if on accounts for hearing down into the analog noise, the S/N indicates a 14 bit performance at best for those tapes. 14 bit or not those tapes, totally scratch my itch. If you want that, we got that and more for your digital pleasure.