Sounds like homework. When is our assignment due? If you already have the data in Matlab then processing it there is going to be much easier, so doing it on an Arduino is make-work.
The Arduino can sample fast enough for basic audio processing. You don't need to slow it down. The normal analogRead() works at about 10kHz if you aren't trying to do any processing during the data-collection time. With some effort, you can get the sample frequency much higher and do some limited processing (like an FIR or IIR) at the same time. The real limitation to sample-then-process is the small amount of memory on the Arduino. High sample rates will chew up all the available SRAM in a fraction of a second.
I use http://t-filter.engineerjs.com/ to design my FIR filters. It's very easy to use that to visualise the result of pass-bands and stop-bands. Then you click the "source code" button and it has everything already programmed in C for you to copy-paste into your Arduino sketch. For some of my projects, I re-write it into a C++ class because it's so easy to do and makes it easier to use the filter in a real project.
If you're already using Matlab to generate the coefficients, then just copy-paste that into the code provided by t-filter. That will get you started.