It's pretty easy to use SigmaStudio to build your signal flow and output the utilized resources. Every time you compile a project, a file called compiler_output.txt is generated in the folder in which your .dspproj file is saved. This file details all of the memory resources used by your current design.
The latest SigmaDSPs (ADAU144x, ADAU1761, ADAU1781) also show this detail in the output window, which shows by default along the right side of the tool. For these ICs, the output also shows exactly how much of each of these memory resources each individual algorithm in your design uses. By looking at this information you can easily see what algorithms can be added, or how much memory you will save by deleting specific blocks.
This FAQ was generated from the following discussion: How to estimate MIPS/Memory resource on SigmaDSP?
Basically yes, The core instruction rate is tied to the internal core rate and that is derived from the MCLK/PLL. So the DSP can only process a finite number of instructions per second. It runs through the entire program every sample period. So if you are running at 96kHz then it is running the program twice during the length of time of one 48kHs sample period. So there are half the instructions available running at 96kHz verses 48kHz fs. 1/4th if you run at 192kHz fs.