Question

A function \( x(t) \) is said to have half-wave odd symmetry if

• A. \( x(t) = -x\left[t \pm \frac{T}{2}\right] \)
• B. \( x(t) = x\left[t - \frac{T}{4}\right] \)
• C. \( x(t) = x\left[t - \frac{T}{2}\right] \)
• D. \( x(t) = -x\left[t + \frac{T}{4}\right] \)

Hint:

Half-wave odd symmetry means that the function is an odd function when shifted by half of its period.

Answer 1

The Correct Option is A

A function \( x(t) \) has half-wave odd symmetry if it satisfies the condition \( x(t) = -x\left[t \pm \frac{T}{2}\right] \), where \( T \) is the period of the function. This symmetry indicates that the function is odd with respect to a half-period shift. Therefore, the correct answer is option (1).