Signals and Systems - Convolution

Let continuous-time signals $x_1(t)$ and $x_2(t)$ be $x_1(t) = \begin{cases} 1, & t \in [0,1] \\ 2-t, & t \in [1,2] \\ 0, & \text{otherwise} \end{cases}$ and $x_2(t) = \begin{cases} t, & t \in [0,1] \\ 2-t, & t \in [1,2]...

Suppose signal y(t) is obtained by the time-reversal of signal x(t), i.e., y(t) = x(−t), −∞ < t < ∞. Which one of the following options is always true for the convolution of x(t) and y(t)?

For the signals x(t) and y(t) shown in the figure, z(t) = x(t) * y(t) is maximum at t = T₁. Then T₁ in seconds is __________. (Round off to the nearest integer).

Let z(t) = x(t) * y(t), where "*" denotes convolution. Let c be a positive real-valued constant. Choose the correct expression for z(ct).

A cascade system having the impulse responses h₁(n) = {1, -1} and h₂(n) = {1, 1} is shown in the figure below, where symbol ↑ denotes the time origin. The input sequence x(n) for which the cascade system produces an outp...