I write this not to engage anyone – I am not interested in a debate. I only write this as testament to experience. With respect to digital filters, it is important to note that there are two separate aspects which may cause confusion to some.
One aspect is the calculation of the coefficients used in the filter program itself – derivation. The other is the implementation of said filter in whatever environment (Purchased digital filter chip, or as a part of a reduced bit DAC or ADC chip). In our case a Schiit written software program runs in a special purpose DSP chip – execution.
Now when the derived filter is running – whether it is optimized for frequency domain, low-pass, high-pass, bandpass, or in our case time and frequency domain that execution is indeed closed form.
The derivation is quite another matter. While researching digital filter derivation before I founded Theta Digital, I found that all frequency domain filters were based upon non closed form math and successive approximations. I looked at many of them none were completely solvable in mathematics. The time domain optimization that Schiit uses was originally posited by Bell Telephone Labs with a publication date of 1917. This is well before there were computers to implement them. This led to a long journey which ended up with the tools to derive the coefficients that generate a filter which not only has closed form solvable math, but which also preserves all of the original samples. I have spent much time researching digital filters, and I am confident that this is the only filter like this. Period. I may now be from a small town, but I have been to county fairs and have actually seen three story buildings
Now, why do this?? It is a lot of work. Five years of my life. Simple. It sounds better. Almost all of the high priced competition uses chips bought from a variety of manufacturers which implement the digital filters. They come with instruction booklets which show you how to hook them up. It's a lot like buying a frozen food entree and reading the side of the box.
I tire of the arguments that since the record side may not be ideal so why bother with good playback. Huh? Let me go back a paragraph. It sounds better! If you agree, then get one. If you don't, then get something else. I have been in this business long enough to know that God could personally appear to me and tell me how to build the perfect audio device and still there will be people who do not like it. There are those obsessed with particular aspects of technology, be they polypropylene capacitors, non-inductive wirewound resistors, FET-Input opamps, Current Feedback opamps, IIR filters, sinc filters, VCXO's, tubes, etc. etc. I am sure I could lose some arguments with some proponents of some technologies.
That said, I have probably produced, designed, and sold more DACs to more people than any other living person. All that is important to me is producing technologically sound products that makes people have fun with music. If you are the guy with a music system that cost more than your car and you only listen to four recordings, all of which you hate because they are not perfect, look elsewhere, please. If you want to debate technology, then do yourself, as well as the poor people who surround you a favor - get out of talking and into action and build something.