Convolution MCQ

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)

  1. c · x(ct) ∗ y(ct)
  2. x(ct) ∗ y(ct)
  3. c · x(t) ∗ y(ct)
  4. c · x(ct) ∗ y(t)
Answer. a

2. x(t) is non-zero only for Tx < t < T’x, and similarly, y(t) is non-zero only for Ty < t < Ty‘. Let z(t) be convolution of x(t) and y(t). Which one of the following statements is true?

  1. z(t) can be non-zero over an unbounded interval.
  2. z(t) is non-zero for t < Tx + Ty
  3. z(t) is zero outside of Tx + Ty < T’x + T’y
  4. z(t) is non-zero for t > T’x > T’y
Answer. c

3. Two systems with impulse responses h1(t) and h2(t) are connected in cascade. Then the overall impulse response of the cascaded system is given by

  1. product of h1(t) and h2(t)
  2. sum of h1(t) and h2(t)
  3. convolution of h1(t) and h2(t)
  4. subtraction of  h2(t) from h1(t)
Answer. c

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

  1. 0
  2. 1/2
  3. 1
  4. 3/2
Answer. a

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

  1. e-t – e-2t
  2. e-3t
  3. e+t
  4. e-t + e-2t
Answer. a

6. The convolution of the functions f1(t) = e-2t u(t) and f2(t) = et u(t) is equal to

  1. -\frac{1}{3}e^{-2t}+\frac{1}{3}e^{t}
  2. \frac{1}{3}e^{-2t}+\frac{1}{3}e^{t}
  3. -\frac{1}{3}e^{-2t}-\frac{1}{3}e^{t}
  4. -\frac{1}{3}e^{t}+\frac{1}{3}e^{-2t}
Answer. a

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