---
title: "Deterministic and random signals"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:deterministic-random-signals"
source: https://www.bctengineer.com/q/semester_5/data_communication/deterministic-random-signals
site: BCT Engineering
---

# Deterministic and random signals

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2073 Chaitra, 4 marks; 2070 Asar, 2 marks (asked 2 times)
- Video: [Deterministic And Random Signals | Classification Of Signals | Signals And Systems](https://www.youtube.com/watch?v=CPeHRjBb_W4) — ENGINEERING TUTORIAL
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/deterministic-random-signals
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Explain deterministic and random signal with example.

## 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.

## Answer

**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.

| Point | Deterministic | Random |
|---|---|---|
| Predictability | Fully predictable | Unpredictable |
| Description | Formula or table | Probability / statistics |
| Information | Carries no new information once known | Information-bearing signals and noise are random |
| Example | sin(ωt) | Noise, speech |

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

## Check yourself

The answer's key points as multiple-choice questions, with the correct option and why.

1. Deterministic signal is
   A. unpredictable
   B. exactly known at every instant
   C. noise
   D. statistical
   Answer: B. Given by formula or table. (Key point: Deterministic)

2. Random signal is described by
   A. a formula
   B. a table
   C. probabilities and averages
   D. sine only
   Answer: C. Mean, variance, autocorrelation. (Key point: Random)

3. Message signals must be
   A. deterministic
   B. constant
   C. periodic
   D. random
   Answer: D. Otherwise no information. (Key point: Information)

## Related in Data Communication

- [Define analog and digital signals](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Aanalog-digital-signal-define) — Data Communication, chapter 1

## Related in other subjects

- [Ergodic process; WSS random signals through LTI](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aergodic-wss-through-lti) — Communication Systems, chapter 9, asked 2×
- [Stochastic process; WSS random signal through LTI](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Astochastic-wss-through-lti) — Communication Systems, chapter 9, asked 2×
- [Classification of measurement signals](https://www.bctengineer.com/question.md?key=semester_4%2Finstrumentation_and_measurement%3Aclassification-of-measurement-signals) — Instrumentation and Measurement, chapter 2
- [USB-SSB expression for a random band limited message](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ausb-ssb-random-message) — Communication Systems, chapter 2