,1. Multiple Choice: What is the Fourier transform of a
continuous-time rectangular pulse signal?
a) Sinc function
b) Step function
c) Delta function
d) Gaussian function
Correct Answer: a) Sinc function
Rationale: The Fourier transform of a rectangular pulse is
a sinc function, which represents the frequency domain
equivalent of the time domain signal.
2. Fill-in-the-Blank: The Laplace transform of a unit step
function, u(t), is _____.
Correct Answer: 1/s
Rationale: The Laplace transform of a unit step function is
1/s, which is derived from the integral definition of the
Laplace transform.
3. True/False: The z-transform is applicable only for
discrete-time signals.
Correct Answer: True
Rationale: The z-transform is indeed only applicable for
discrete-time signals as it maps the discrete-time signal into
the complex frequency domain.
, Differentiation
Rationale: The Fourier series has properties of linearity,
time shifting, and differentiation. Frequency shifting is not a
property of the Fourier series but of the Fourier transform.
5. Multiple Choice: In a linear time-invariant (LTI) system, if
the input is a sinusoidal signal, the output will be:
a) A sinusoidal signal of the same frequency
b) A sinusoidal signal of a different frequency
c) A constant signal
d) A ramp signal
Correct Answer: a) A sinusoidal signal of the same
frequency
Rationale: In an LTI system, the frequency of a sinusoidal
input signal is preserved at the output.
6. Fill-in-the-Blank: The impulse response of an LTI system
is its output when the input is a _____.
Correct Answer: delta function
Rationale: The impulse response of an LTI system is
defined as the output when the input is a delta function,
representing the system's response to a unit impulse.
7. True/False: Convolution in the time domain is equivalent
to multiplication in the frequency domain.
Correct Answer: True
Rationale: Convolution in the time domain corresponds to
multiplication in the frequency domain, as per the
convolution theorem.
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