Question:
A signal that exists only for a finite duration of time is called:
A signal that exists only for a finite duration of time is called:
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All finite-duration signals are automatically non-periodic (aperiodic) because repetition requires an infinite time horizon to satisfy \(x(t) = x(t+T)\) everywhere.
Updated On: Jun 23, 2026
- Periodic
- Aperiodic
- Even
- Causal
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The Correct Option is B
Solution and Explanation
Concept:
Signals are classified based on their behavior over time:
• Periodic Signal: Satisfies the condition \(f(t) = f(t + T)\) for all values of \(t\), where \(T\) is a fixed positive non-zero fundamental time period. This definition implies that the signal must repeat its pattern continuously from \(t = -\infty\) to \(t = +\infty\).
• Aperiodic (Non-Periodic) Signal: Any signal that fails to satisfy the periodic condition. This category includes transient waveforms, single pulses, or signals that exist only for a restricted, finite duration of time and do not repeat.
• Even Signal: Demonstrates reflective symmetry across the vertical axis, satisfying the condition \(f(-t) = f(t)\).
• Causal Signal: A signal that is identically zero for all negative time values, satisfying \(f(t) = 0\) for \(t < 0\).
Step 1: Analyzing the problem constraint.
The question specifies a signal that "exists only for a finite duration of time." This means there exist bounds \(t_1\) and \(t_2\) such that the signal profile is non-zero only within that window, and zero everywhere else: \[ x(t) = 0 \quad \text{for } t t_2 \]
Step 2: Testing against the definitions.
Because the signal terminates and stays at zero outside this finite window, it cannot repeat itself identically at regular intervals across an infinite time domain. Therefore, it cannot be periodic. Any signal that is not periodic is classified as an aperiodic signal. This matches Option (B).
• Periodic Signal: Satisfies the condition \(f(t) = f(t + T)\) for all values of \(t\), where \(T\) is a fixed positive non-zero fundamental time period. This definition implies that the signal must repeat its pattern continuously from \(t = -\infty\) to \(t = +\infty\).
• Aperiodic (Non-Periodic) Signal: Any signal that fails to satisfy the periodic condition. This category includes transient waveforms, single pulses, or signals that exist only for a restricted, finite duration of time and do not repeat.
• Even Signal: Demonstrates reflective symmetry across the vertical axis, satisfying the condition \(f(-t) = f(t)\).
• Causal Signal: A signal that is identically zero for all negative time values, satisfying \(f(t) = 0\) for \(t < 0\).
Step 1: Analyzing the problem constraint.
The question specifies a signal that "exists only for a finite duration of time." This means there exist bounds \(t_1\) and \(t_2\) such that the signal profile is non-zero only within that window, and zero everywhere else: \[ x(t) = 0 \quad \text{for } t t_2 \]
Step 2: Testing against the definitions.
Because the signal terminates and stays at zero outside this finite window, it cannot repeat itself identically at regular intervals across an infinite time domain. Therefore, it cannot be periodic. Any signal that is not periodic is classified as an aperiodic signal. This matches Option (B).
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