So u have to take the 16th notes in 4/4 as the new pulse in 7/16 or 5/16, then the 8th notes in 4/4 for the 3/8 pulse. This is provided that there are no markings stating otherwise.

If these time sig changes are consecutive bars, 7 + 5 = 12/16 which is equal to 6/8. Add the 3/8 bar and it’s 9/8 total. But, without seeing the chart, this way of thinking may not work do to rhythmic phases within 7, 5, and 3/8. My guess is that this is true or it wouldn’t have been written that way. In the end it’s a great exercise in counting. Once you sort it (go slow), it won’t be so bizarre.