What the terms Basis functions and Orthogonal denote in case of signals?

1. What is orthogonal function in signals and systems?
2. What are orthogonal basis functions?
3. What is a basis function in signal processing?
4. What does it mean when signals are orthogonal?
5. What is meant by basis function?
6. What is signal approximation using orthogonal functions?

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.

What are orthogonal basis functions?

In functional analysis, an orthogonal basis is any basis obtained from an orthonormal basis (or Hilbert basis) using multiplication by nonzero scalars.

What is a basis function in signal processing?

▶ A basis for a class of signals is a collection of M signals in the class that have the property that any other signal in that class can be written as a weighted sum of those signals. x[n] = M−1. ∑ k=0.

What does it mean when signals are orthogonal?

In a nutshell, two signals are orthogonal if the inner product between them (namely, the integral I wrote above) is 0, and the vectors/arrays obtained by sampling them tell us nothing about their being orthogonal.

What is meant by basis function?

In mathematics, a basis function is an element of a particular basis for a function space. Every function in the function space can be represented as a linear combination of basis functions, just as every vector in a vector space can be represented as a linear combination of basis vectors.

What is signal approximation using orthogonal functions?

Let a function f(t), it can be approximated with this orthogonal signal space by adding the components along mutually orthogonal signals i.e. f(t)=C1x1(t)+C2x2(t)+... +Cnxn(t)+fe(t)