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In the context of electrical signals, if the signal generated has a definite pattern that repeats itself at regular intervals of time, such a signal is called ______.
periodic signal
independent signal
dependent signal
non-periodic signal
periodic signal
A periodic signal is defined as a signal that repeats its values at regular intervals of time. This repetition occurs because the signal adheres to a specific functional pattern that cycles indefinitely.
A periodic signal is defined as a signal that repeats its values at regular intervals of time. This repetition occurs because the signal adheres to a specific functional pattern that cycles indefinitely.
x(t)=x(t+T) тАФ definition of a periodic signal where T is the fundamental period
f=T1тАЛ тАФ relationship between frequency and time period
A signal x(t) is periodic if there exists a positive constant T (the fundamental period) such that x(t)=x(t+T) for all t. The reciprocal of the fundamental period, f=T1тАЛ, determines the frequency of the signal in Hertz.
Periodic signals must satisfy the condition x(t)=x(t+nT) where n is any integer.
The smallest positive value of T that satisfies the condition is called the fundamental period.
Non-periodic signals are signals that do not exhibit any repetitive pattern over time.
Allows for easy frequency domain analysis using Fourier series.
Provides predictability in electronic system behavior.
Real-world signals are rarely perfectly periodic due to noise and transient disturbances.
Requires infinite duration for strict mathematical periodicity.
AC power distribution systems
Clock signals in digital circuits
Communication signal processing
Option B and C (independent/dependent signals) are classifications based on system variables, not time-domain repetition.
Option D (non-periodic/aperiodic signal) refers to signals that never repeat their pattern.
A is correct тАФ A periodic signal is characterized by a waveform that repeats itself exactly after a fixed duration known as the period.
When solving signal analysis problems, always check if x(t)=x(t+T) holds for all t to confirm periodicity; if a constant T cannot be found, the signal is aperiodic.
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