How can I approximate a signal

1. How do you approximate a signal using orthogonal functions?
2. What is orthogonal function in signals and systems?

How do you approximate a signal using orthogonal functions?

As these functions are orthogonal to each other, any two signals x_j(t), x_k(t) have to satisfy the orthogonality condition. i.e. Let a function f(t), it can be approximated with this orthogonal signal space by adding the components along mutually orthogonal signals i.e. All terms that do not contain C_k is zero.

What is orthogonal function in signals and systems?

In general, a signal set is said to be an orthogonal set if (s_k,s_j) = 0 for all k ≠ j. A binary signal set is antipodal if s₀(t) = −s₁ (t) for all t in the interval [0,T]. Antipodal signals have equal energy E, and their inner product is (s₀,s₁) = −E.