Consider the following sentences regarding a periodic signala) A periodic signal always repeats itself after minimum fundamental time period T.b) A periodic signal is exist from -∞ to +∞ and converse is also true.c) A periodic signal exist from -∞ to +∞.Which of the following is/are correct option?a)A and Cb)A,B and Cc)A and Bd)B and CCorrect answer is option 'A'. Can you explain this answer?

Question

Answer

Understanding Periodic Signals
Periodic signals are fundamental in signal processing and communication theory. Here, we evaluate the correctness of the provided statements regarding periodic signals.
Statement A: A periodic signal always repeats itself after a minimum fundamental time period T.
- This statement is correct.
- A periodic signal is defined as one that repeats itself at regular intervals, characterized by its fundamental period T. This means after every T seconds, the signal waveform is identical.
Statement B: A periodic signal exists from -∞ to +∞ and converse is also true.
- This statement is incorrect.
- While periodic signals can exist over the entire time axis (from -∞ to +∞), the converse is not valid. Not all signals that exist from -∞ to +∞ are periodic; many signals are non-repeating and thus not periodic.
Statement C: A periodic signal exists from -∞ to +∞.
- This statement is also incorrect.
- While periodic signals can technically extend infinitely, they do not have to. A periodic signal can be defined over a finite interval and may not explicitly cover the entire time range from -∞ to +∞.
Conclusion
Based on the evaluation:
- Correct Option: A and C are incorrect, only A is correct.
- Therefore, the correct answer is option A: Only statement A is true regarding periodic signals.
Understanding these distinctions helps in grasping the properties and behavior of signals in various applications.

Answer

A- Is the definition of any periodic signal.

B- A periodic signal is only exist from -∞ to +∞ and converse is not true because any signal or anything practically always take birth from origin means from it increases. If it comes from positive to negative then it is a decaying signal not a periodic signal. Thus, option A is the correct answer.

Similar GATE Doubts

Consider the following sentences regarding a constant signal.1) A constant signal is a periodic signal because it has no fundamental period.2) A constant signal is an anti periodic signal because it never repeats itself.

A continuous –time function x(t) is periodic with period T. The function is sampled uniformly witha sampling period Ts. In which one of the following cases is the sampled signal periodic ?

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