Bounded Signal & Unbounded Signal

Bounded Signal is a signal which is having a finite value at all instants of time. Consider a continuous-time signal x(t) such that x(t) has finite-amplitude (value) at all time (t) as shown in figure 1 is an example of the bounded signal.

Bounded signal
Figure 1. Bounded signal

Examples of bounded signals are sin(t), cos(t), u(t). All these three signals are bounded by an amplitude of value 1. ( The maximum possible value is 1). Signals, 5 sin(t), 5 cos(t), 5 u(t) similarly are bounded by a value of 5.

Unbounded Signal is a signal which is having an infinite value at any instant of time. Consider a continuous-time signal x(t) such that x(t) has infinite-amplitude (value) at t= infinite as shown in figure 2 is an example of the unbounded signal.

Unbounded signal
Figure 2. Unbounded signal

Examples of unbounded signals are tan(t), cot(t), sec(t), cosec(t), r(t), δ(t). All these signals have infinite value as maximum possible value.

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