1. 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)

- c · x(ct) ∗ y(ct)
- x(ct) ∗ y(ct)
- c · x(t) ∗ y(ct)
- c · x(ct) ∗ y(t)

2. x(t) is non-zero only for T_{x} < t < T’_{x}, and similarly, y(t) is non-zero 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?

- z(t) can be non-zero over an unbounded interval.
- z(t) is non-zero for t < T
_{x}+ T_{y} - z(t) is zero outside of T
_{x}+ T_{y}< T’_{x}+ T’_{y} - z(t) is non-zero for t > T’
_{x}> T’_{y}

3. Two systems with impulse responses h_{1}(t) and h_{2}(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

- product of h
_{1}(t) and h_{2}(t) - sum of h
_{1}(t) and h_{2}(t) - convolution of h
_{1}(t) and h_{2}(t) - subtraction of h
_{2}(t) from h_{1}(t)

4. Let y[n] denotes the convolution of h[n] and g[n], where h[n] = (1/2)^{n} u[n] and g[n] is a causal sequence. If y[0] = 1 and y[1] = 1/2, then g[1] equals

- 0
- 1/2
- 1
- 3/2

5. Given two continous time signals x(t) = e^{-t} and y(t) = e^{-2t} which exist for t > 0, the convolution z(t) = x(t) ∗ y(t) is

- e
^{-t}– e^{-2t} - e
^{-3t} - e
^{+t} - e
^{-t}+ e^{-2t}

6. The convolution of the functions f_{1}(t) = e^{-2t} u(t) and f_{2}(t) = e^{t} u(t) is equal to

- $-\frac{1}{3}e^{-2t}+\frac{1}{3}e^{t}$
- $\frac{1}{3}e^{-2t}+\frac{1}{3}e^{t}$
- $-\frac{1}{3}e^{-2t}-\frac{1}{3}e^{t}$
- $-\frac{1}{3}e^{t}+\frac{1}{3}e^{-2t}$