I am a beginner in digital communications and I have a question on the pulse shaping filter.
For example, I have an orthogonal family $ \{s_1,...,s_N \}$. Can we preserve the orthogonality with a pulse shaping filter $g$ as a raised cosine filter, that is to say the family $ \{ g(n) \ast s_1(n),...,g(n) \ast s_N(n) \}$ is orthogonal?