Mainstream DAC runs like this:
FIR interpolation:
44.1 → 88.2 → 176.4 → 352.8
Each of those stages having roughly half of the filter taps of the previour. If your input rate is higher than 44.1k, then skip the applicable number of stages from the beginning. If the rate is 352.8k or higher, the digital filter is skipped.
Then from 352.8k to the modulator rate, just copy the same sample as many times as necessary. This is like a NOS PCM DAC, so it creates images at multiples of the 352.8k rate.
Some chips just run 8x filter for input rates 44.1, 88.2 and 176.4. So 44.1 becomes 352.8, 88.2 becomes 705.6 and 176.4 becomes 1411.2. While modulator runs at the same rate always, thus the number of times each sample gets repeated varies. For input rates 352.8k or higher, the filter is skipped.
44.1 → 705.6 and then linear interpolation (straight lines) / 2nd order IIR from 705.6 to the modulator rate.
Yes, it’s a regular SDM DAC. Of course each manufacturer has their own marketing name.