Welcome to CoffeeSnobs.
Filtering comes in many shapes and sizes, and without knowing the specifics of yours and the specifics of your water, any judgement is only guessing. Most under-sink filters will not change the hardness of the water at all.
Most filters will take out sediment, some filtering also takes out most dissolved minerals (reverse osmosis) and is not recommended without replacing some of the minerals. Some r.o. water can taste flat and consuming too much can reportedly leave you short of essential minerals. It also can harm espresso machines.
IIRC the recommended level of mineralisation for taste and safe use is about 50-75 ppm.
For what its worth I put all my espresso water through a .5 micron charcoal filter, after it has had the mineral content balanced. Charcoal filters this fine take out most solids and the resulting water is clear and tastes fine.
I hope this helps.
Post some specifics about your filter and machine and Im sure some targeted help will be forthcoming.