# orthogonal family and pulse shaping filter

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?

• What is your definition off an orthogonal family? Please do not reply with a flippant answer such as "$s_i$ and $s_j$ are orthogonal for $I\neq j$" but incorporate real details into your question explaining how exactly they are orthogonal with details of the inner product ($\langle s_i, s_j\rangle = 0$ is not enough). – Dilip Sarwate Mar 25 '19 at 13:52