Signals and Systems – Multiple Choice Questions (MCQs)

1. 37. Which of the following systems is linear?

   • A. y(t) = x²(t)
   • B. y(t) = 2x(t) + 3
   • C. y(t) = cos(x(t))
   • D. y(t) = t * x(t)

2. 38. The impulse response of an ideal low-pass filter is a:

   • A. Sinc function
   • B. Unit step function
   • C. Exponential function
   • D. Impulse function

3. 39. The energy of a signal x(t) is given by:

   • A. ∫|x(t)| dt
   • B. ∫x²(t) dt
   • C. ∫|x(t)|^2 dt
   • D. ∫x(t) dt

4. 40. The power of a signal x(t) is given by:

   • A. lim(T->∞) (1/T) ∫|x(t)| dt
   • B. lim(T->∞) (1/T) ∫x²(t) dt
   • C. lim(T->∞) (1/T) ∫|x(t)|^2 dt
   • D. lim(T->∞) ∫x(t) dt

5. 41. Differentiation in the time domain corresponds to multiplication by ________ in the Laplace domain.

   • A. s
   • B. 1/s
   • C. e^s
   • D. e^-s

6. 42. Integration in the time domain corresponds to division by ________ in the Laplace domain.

   • A. s
   • B. 1/s
   • C. e^s
   • D. e^-s

7. 43. The time-shift property of Fourier Transform states that a shift in time corresponds to a ________ in frequency domain.

   • A. Phase shift
   • B. Amplitude change
   • C. Frequency shift
   • D. Scaling

8. 44. The frequency-shift property of Fourier Transform states that a shift in frequency corresponds to a ________ in time domain.

   • A. Phase shift
   • B. Amplitude change
   • C. Multiplication by an exponential
   • D. Scaling

9. 45. The relationship between continuous-time Fourier Transform X(jΩ) and discrete-time Fourier Transform X(e^jω) for sampled signals is:

   • A. X(e^jω) = X(jΩ)
   • B. X(e^jω) = (1/T) Σ X(j(ω-2πk)/T)
   • C. X(e^jω) = X(jωT)
   • D. X(e^jω) = X(jΩ/T)

10. 46. An ideal differentiator has a frequency response magnitude that is proportional to:

    • A. ω
    • B. 1/ω
    • C. ω²
    • D. 1/ω²

11. 47. An ideal integrator has a frequency response magnitude that is proportional to:

    • A. ω
    • B. 1/ω
    • C. ω²
    • D. 1/ω²

12. 48. The convolution of a signal x(t) with an impulse δ(t-t0) is:

    • A. x(t)
    • B. x(t-t0)
    • C. x(t+t0)
    • D. δ(t-t0)