Deterministic and Random Signals – Definition, Examples & Differences

Deterministic & Random Signals

Deterministic Signal:

A signal which has no uncertainty at any given instant of time is called a deterministic signal.

Ex:$$x(t)=A\cos \omega t \qquad \text{for } -\infty < t < \infty$$

At any given time, the behaviour of the signal can be predicted. So, for a deterministic signal, the amplitude value of $x(t)$ can be computed. The pattern of deterministic signal is regular and can be characterised mathematically (i.e. can be put in an equation).

Non-Deterministic Signal (Random Signal)

A non-deterministic signal is a signal whose behaviour cannot be predicted in advance. The pattern of a random signal is quite irregular. Random signals are also known as non-deterministic signals.

Examples of Random Signals

• Noise generated in the amplifier of a radio receiver.
• ECG signal (heart-beat signal).
• Speech signal.
• Weather noise and atmospheric noise.

Important Points to Note

• The value of a random signal cannot be predicted at any given instant of time.
• It contains some degree of uncertainty.
• Its behaviour is irregular and cannot be represented by a single mathematical equation.
• Random signals are analysed using statistical methods rather than exact mathematical expressions.

Difference Between Deterministic and Random Signals

Deterministic Signal	Random Signal
Its value can be predicted exactly at any given time.	Its value cannot be predicted exactly at any given time.
There is no uncertainty about its behaviour.	There is some uncertainty about its behaviour.
Usually follows a known and regular pattern.	Usually has an irregular or unpredictable pattern.
Can be described using a mathematical equation.	Is generally described using probability and statistical properties.
Example: x(t) = A cos(ωt)	Examples: noise, speech signal, and ECG signal.
Also called a predictable signal.	Also called a non-deterministic signal.