You don't need to filter to get clear homebrew.
Add rehydrated Irish moss or a Whirlfloc tablet in the last 5 minutes of the boil. Alternatively, there's a (Australian?) product called BeerBrite, which appears to be unobtanium for home brewers in the USA, but for which a DIY recipe is half a Whirlfloc tablet crushed and mixed with 2.5 g Polyclar VT (PVPP) in 1/2 cup water, also added to end of boil.
White Labs Clarity Ferm is an enzyme you can add when pitching yeast, that reduces chill haze.
After fermentation, dry hopping, etc., chill the beer. A lot of the haze will precipitate out and collect on the bottom; rack the beer off it.
For even more clearing, after the cold crash, mix 1 tsp of non-flavored gelatin in 1/2 cup H2O and carefully heat to no more than 155 F (I do consecutive 10-sec bursts in a microwave) and add it to the cold beer, and let sit for a couple of days. The gelatin has an electrical charge opposite to that of "stuff" dissolved in the beer, so it clumps together and makes it heavy enough to precipitate out. Rack the beer into the bottling bucket.
As mentioned above, bottle conditioning (carbonation) generates a *new* set of mini-trub at the bottom of each bottle. Carefully pour the beer into a glass except for the last half inch; toss that. This is also why you have to clean the bottles well if you're going to reuse them. Homebrew bottles have a trub in the bottom that commercial bottles don't, and sometimes it will stick around after a casual rinse.
I usually do the DIY BeerBrite, cold crash, and gelatin fining. I only use Clarity Ferm when brewing a really light (as in SRM) ale. The beer is so clear I quit using the ubiquitous Red Solo Cup when I take my homebrew on outings -- I use clear plastic glasses so that beautiful, clear beer shines through!!! Damn, now I'm thirsty...