Orthogonal basis of signal space and the projection of white noise

1. What is orthogonal signal space?
2. Why do we need an orthogonal basis for projection?
3. What is orthogonality of signals?
4. What is orthogonal signal in digital communication?

What is orthogonal signal space?

Orthogonal Signal Space

Let us consider a set of n mutually orthogonal functions x₁(t), x₂(t)... x_n(t) over the interval t₁ to t₂. 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. ∫t2t1xj(t)xk(t)dt=0wherej≠k.

Why do we need an orthogonal basis for projection?

The usefulness of an orthonormal basis comes from the fact that each basis vector is orthogonal to all others and that they are all the same "length". Consider the projection onto each vector separately, which is "parallel" in some sense to the remaining vectors, so it has no "length" in those vectors.

What is orthogonality of signals?

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. Many of the baseband signal sets of interest can be defined in terms of a single waveform v(t).

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.