Periodic and Non-Periodic Signals | Course: Signals & Systems

Periodic Signal

Periodic Signal:
A signal which repeats itself after a fixed time period is called a periodic signal.

Condition of Periodicity

A signal $x(t)$ is periodic if:$$x(t) = x(t+T)$$

where,

• $T$ = Time period of $x(t)$

The smallest positive value of TT for which the above condition is satisfied is called the fundamental time period of the signal.

Examples of Periodic Signals

Some common examples of periodic signals are:

Classification of Periodic Signals

Periodic signals can be classified into two types:

Periodic DT Signal

Periodic DT Signal: Condition of periodicity is given as:

where N = period of the signal.

Non-periodic Signal

Non-periodic signal: A non-periodic signal is also known as an aperiodic signal. A non-periodic signal doesn’t satisfy the condition:

So, for a non-periodic signal,

Non-periodic Signal

A non-periodic signal can be classified into two types:

• Continuous-time non-periodic signal
• Discrete-time non-periodic signal

Discrete Non-periodic Signal

Discrete non-periodic signal:

Condition:

where:

• $x(n)$ = DT signal
• $n$ = integer
• $n$ = discrete-time variable
• $N$ = period of DT signal