How can we generate an orthogonal sinusodial signal to any other signal?

1. How do you prove two signals are orthogonal?
2. How do you approximate a signal using orthogonal functions?
3. What does it mean for signals to be orthogonal?
4. What is orthogonal signal in digital communication?

How do you prove two signals are orthogonal?

Two signals are orthogonal if 〈y(t),x(t)〉 = 0. (Pythagorean Theorem). If signals x(t) and y(t) are orthogonal and if z(t) = x(t) + y(t) then Ez = Ex + Ey. x(t)y(t)dt = 0.

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 does it mean for signals to be orthogonal?

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.

What is orthogonal signal in digital communication?

Orthogonal signals are used extensively in the communications industry. They range from a simple sine/cosine quadrature signals to multiple signals whose inner product is equal to zero. Orthogonal signals can be used for several different applications.