Question

The orthogonal signals S1 and S2 satisfy the following relation.

• A. \( \int_{0}^{T} s_1(t)s_2(t) dt = 0 \)
• B. \( \int_{0}^{T} |s_1(t)s_2(t)| dt = 1 \)
• C. \( \int_{-\infty}^{\infty} |s_1(t)s_2(t)| dt = \infty \)
• D. Both (b) and (c)

Hint:

Orthogonality is a condition of two signals, with zero cross correlation over an interval. \( \int_{0}^{T} s_1(t)s_2(t) dt = 0 \)

Answer 1

The Correct Option is A

Two signals \( s_1(t) \) and \( s_2(t) \) are considered orthogonal over an interval [0, T] if their product integrated over that interval is equal to zero, which is mathematically represented as \( \int_{0}^{T} s_1(t)s_2(t) dt = 0 \). This is a mathematical property for signals which is essential in many digital communication systems.