Question about filtering polished spirit

[naeco]

I doubled distilled a sugar wash with a friends potstill and really wanted something as neutral as possible. Even after 2 distillation, I still had that weird taste and smell in the finale spirit and I dont have access to my friends still for a couple months so I purchased some activated carbon online and dumped 3/4 cup in my 3.5 liter of spirit diluted a 42%. I didn't know I was supposed to clean the carbon before putting it in the carboy so I ended up with lots of carbon dust in suspension.

It's been 4 days now and the smell is 90% gone so I plan on flavoring my spirit next Wednesday but was concerned about all the carbon dust in suspension. What do I use to filter out the carbon and make sure I even trap the dust particle ?

Can I simply use coffee filters and maybe do it twice or even 3 times until fully clear or will the black dust never go away ?

Thanks in advance,

naeco