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Deterministic and random signals

Short answer

Deterministic signal is exactly predictable from a mathematical expression, e.g., A sin(2πft). Random signal is unpredictable, described only by statistics (mean, variance); e.g., thermal noise. Information-bearing signals are random.

Explain deterministic and random signal with example.

Deterministic signal: a signal whose value at every instant is exactly known from a mathematical expression, a graph or a table. It can be predicted for any time. Examples: x(t) = A sin(2πft), a unit step, a square wave from a function generator.

Random (stochastic) signal: a signal whose value at any instant cannot be predicted exactly; it can be described only by probabilities and statistical averages (mean, variance, autocorrelation). Examples: thermal noise in a resistor, a speech signal, the received signal in a fading channel.

PointDeterministicRandom
PredictabilityFully predictableUnpredictable
DescriptionFormula or tableProbability / statistics
InformationCarries no new information once knownInformation-bearing signals and noise are random
Examplesin(ωt)Noise, speech

Message signals must be random (otherwise there would be no information to send); carriers are deterministic.

✓ Answer checked by Claude Opus 5.5 (high effort)

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