The original DS:
44.1/48 to 88.2/96 (Nyquist rate cutoff)
88.2/96 to 176.4/192 (Nyquist rate cutoff)
176.4/192 to 28.224MHz (direct zero stuffing) (Butterworth IIR)
Decimation by 5
Somewhat later:
44.1/48/88.2/96 to 176.4/192 (Nyquist rate cutoff)
176.4/192 to 28.224MHz (direct zero stuffing) (Butterworth IIR)
Decimation by 5
Somewhat later:
44.1/48/88.2/96/176.4/192 to 352.8/384 (Nyquist rate cutoff)
352.8/384 to 56.448MHz (direct zero stuffing) (no more Butterworth IIR, not needed for 44.1…, good enough for 48…)
Decimation by 5
The system as a whole sounded better by dropping the Butterworth IIR
There aren’t enough multiplies available to do a respectable FIR filter at 56.448MHz. The system sounded better without an IIR in spite of some (pretty high frequency) low level aliasing.
For the Mk II I wanted to do the 48… properly. (It was already proper to zero stuff 705.6kHz to 11.2896MHz and then SDM.) But 48… would take more work, especially since I’d need to go to 112.896MHz if I only took one step. The answer was to take as big a step as possible at the lower frequencies and then take a smaller step if I needed to. The decimation by 5 would be early enough that it didn’t compromise the quality of the output, which precluded it from being used on 786kHz because that would have a filter cutoff out at 76.8kHz.
The upsampling needed to be 147/10 which is (3 * 7 * 7) / (2 * 5)
The biggest first step would be 49 and then 3, but then we’d need to be filtering at 37.632MHz.
The 2nd choice would be 3 * 7 or 21 and then 7 which is what I did.
Then I needed to put in the decimation by 2 and the decimation by 5.
Since the spec for the DS Mk II doesn’t support 384, decimating 768 to 384 wouldn’t lose anything so I could do it first. Decimating by 5 there wouldn’t be good.
So the 48… recipe became 48/96/192 to 768kHz and then 768 / 2 * 21 / 5 * 7 = 11.2896Mhz.
I’d like to add 384k and possibly even 768, but that won’t be for a release or two if I do do it.