x(t) is nonzero only for Tx < t < T'x, and similarly,

Home » Signals and Systems » Signals and systems electrical engineering miscellaneous » Question

x(t) is nonzero only for T_x < t < T'_x, and similarly, y(t) is nonzero only for T_y < t < T'_y. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is TRUE?

1. z(t) can be nonzero over an unbonded interval
2. z(t) is nonzero for t < T_x + T_y
3. z(t) is zero outside of T_x + T_y < t < T'_x + T'_y
4. z(t) is nonzero for t > T'_x + T'_y

Correct Option: C

Given that z(t) is x(t)* y(t)
Range of z(t) is [sum of lower limits of x(t) and y(t) to sum of upper limit of x(t) and y(t)].
T_x + T_y < t < T_x + T_y