---
title: "Causal, non-causal and anticausal systems"
subject: "Data Communication"
chapter: 2
key: "semester_5/data_communication:causal-anticausal"
source: https://www.bctengineer.com/q/semester_5/data_communication/causal-anticausal
site: BCT Engineering
---

# Causal, non-causal and anticausal systems

Data Communication · Chapter 2: Signals and Systems

- Asked in: 2076 Chaitra, 10 marks; 2072 Kartik, 6 marks (asked 2 times)
- Video: [Causal and Non-Causal Systems](https://www.youtube.com/watch?v=mqwUtn5cip8) — Neso Academy
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/causal-anticausal
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-2

## Question

Explain the properties of causal, non-causal and anticausal systems with example.

## Short answer

Causal systems use only present/past inputs (h(t)=0 for t<0; e.g., y(t)=x(t)+x(t-2)). Non-causal use future inputs (e.g., y(t)=x(t+1)). Anticausal systems use only future/present inputs (h(t)=0 for t>0; e.g., y(t)=x(t+3)).

## Answer

#### Causal system
The output at any time depends only on the present and past values of the input (and past outputs). It does not need the future. All physical real-time systems are causal. For an LTI system, h(t) = 0 for t < 0.
- Example: y(t) = x(t) + x(t - 2); h(t) = e^(-t)u(t).

#### Non-causal system
The output depends on at least one future value of the input. Such systems cannot be built for real-time use but can be used in offline processing (stored data, image processing). For an LTI system, h(t) ≠ 0 for some t < 0.
- Example: y(t) = x(t + 1), or y(t) = x(t) + x(t + 2).

#### Anticausal system
The output depends only on the present and future values of the input; no past value is used. For an LTI system, h(t) = 0 for t > 0.
- Example: y(t) = x(t + 3); h(t) = e^(at)u(-t).

```text
Causal      h(t): ........|=====\___   (t >= 0 only)
Anticausal  h(t): ___/====|........   (t <= 0 only)
Non-causal  h(t): ___/====|====\___   (both sides)
```

A system that is anticausal is non-causal (except for the memoryless case), but a non-causal system is not necessarily anticausal.

## Check yourself

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

1. Causal LTI h(t) satisfies
   A. h(t)=0 for t>0
   B. h(t)=0 for t<0
   C. h(t)!=0 for t<0
   D. h(t) infinite
   Answer: B. Only present and past inputs. (Key point: Causal)

2. Anticausal LTI h(t) satisfies
   A. h(t)=0 for t<0
   B. h(t)=0 always
   C. h(t)=0 for t>0
   D. h(t)=1
   Answer: C. Uses present and future inputs only. (Key point: Anticausal)

3. Non-causal systems can be used for
   A. real-time hardware
   B. all physical systems
   C. none
   D. offline processing of stored data
   Answer: D. They cannot run in real time. (Key point: Non-causal use)

4. Which is true?
   A. Anticausal is non-causal, but not conversely
   B. Non-causal is always anticausal
   C. Causal is anticausal
   D. They are identical
   Answer: A. Non-causal includes both sides of h. (Key point: Relationship)

## Related in Data Communication

- [Basic properties of systems](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Asystem-properties) — Data Communication, chapter 2, asked 3×
- [Check properties of y(t) = t·x(t-1)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Acheck-t-xt-1) — Data Communication, chapter 2
- [Invertibility; properties of y[n], y(t)](https://www.bctengineer.com/question.md?key=semester_5%2Fdata_communication%3Ainvertibility-system-properties) — Data Communication, chapter 2

## Related in other subjects

- [Classification of systems; ideal LPF is non-causal](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Aclassify-systems-ideal-lpf) — Communication Systems, chapter 1
- [Short note: Causal and non-causal systems](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Ashort-note-causal-noncausal) — Signals and Systems, chapter 5
- [Hilbert transform; ideal LPF is non-causal](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Ahilbert-ideal-lpf-noncausal) — Communication Systems, chapter 1
- [Convolution sum; ideal LPF is non-causal](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aconvolution-sum-ideal-lpf-noncausal) — Signals and Systems, chapter 5