Question

In the table shown below, match the signal type with its spectral characteristics.

\[ \begin{array}{|l|l|} \hline \text{Signal type} & \text{Spectral characteristics} \\ \hline (i) \; \text{Continuous, aperiodic} & (a) \; \text{Continuous, aperiodic} \\ \hline (ii) \; \text{Continuous, periodic} & (b) \; \text{Continuous, periodic} \\ \hline (iii) \; \text{Discrete, aperiodic} & (c) \; \text{Discrete, aperiodic} \\ \hline (iv) \; \text{Discrete, periodic} & (d) \; \text{Discrete, periodic} \\ \hline \end{array} \]

• A. (i) $\to$ (a), (ii) $\to$ (b), (iii) $\to$ (c), (iv) $\to$ (d)
• B. (i) $\to$ (a), (ii) $\to$ (c), (iii) $\to$ (b), (iv) $\to$ (d)
• C. (i) $\to$ (d), (ii) $\to$ (b), (iii) $\to$ (c), (iv) $\to$ (a)
• D. (i) $\to$ (a), (ii) $\to$ (c), (iii) $\to$ (d), (iv) $\to$ (b)

Hint:

Rule of thumb: Periodic in time $\Rightarrow$ discrete in frequency, Aperiodic in time $\Rightarrow$ continuous in frequency. Same holds for discrete-time signals with reversed roles.

Answer 1

The Correct Option is A

Step 1: Fourier Transform properties.
- A continuous aperiodic signal $\;\;\Rightarrow\;\;$ continuous aperiodic spectrum.
- A continuous periodic signal $\;\;\Rightarrow\;\;$ discrete spectrum.
- A discrete aperiodic signal $\;\;\Rightarrow\;\;$ continuous periodic spectrum.
- A discrete periodic signal $\;\;\Rightarrow\;\;$ discrete spectrum.
Step 2: Match.
(i) Continuous, aperiodic $\to$ (a) Continuous, aperiodic.
(ii) Continuous, periodic $\to$ (b) Continuous, periodic.
(iii) Discrete, aperiodic $\to$ (c) Discrete, aperiodic.
(iv) Discrete, periodic $\to$ (d) Discrete, periodic.
\[ \boxed{(A)\;\; (i)\to(a),\; (ii)\to(b),\; (iii)\to(c),\; (iv)\to(d)} \]