It also speaks of imparted righteousness (Matthew 5:6, Romans 5:19, 1 John 3:7). Faith produces a righteous heart; and it is speaking of real righteousness, not pretend.
My understanding is that in imputing righteousness to us, God will not be far behind with imparting righteousness to us also. He declares us righteous; and since it is impossible for the Lord to lie (Titus 1:2, Hebrews 6:18), He is calling those things which are not as though they are (Romans 4:17); thus creating a new reality, that the person is righteous with the righteousness of faith, fine linen clean and white (Revelation 19:8). The righteousness of faith is a faith that exceeds that of the scribes and Pharisees in the practical sense (see Matthew 5:20); since it is a righteousness that has to do with thoroughly cleansing (Psalms 51:7) the inside of the cup and platter rather than just the outside.