---
title: "Short note: Causal and non-causal systems"
subject: "Signals and Systems"
chapter: 5
key: "semester_4/signals_and_systems:short-note-causal-noncausal"
source: https://www.bctengineer.com/q/semester_4/signals_and_systems/short-note-causal-noncausal
site: BCT Engineering
---

# Short note: Causal and non-causal systems

Signals and Systems · Chapter 5: Continuous-Time Systems

- Asked in: 2075 Bhadra, 3 marks
- 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_4/signals_and_systems/short-note-causal-noncausal
- Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-5

## Question

Write a short note on causal and non causal systems.

## Short answer

Causal system output depends only on present and past inputs; non-causal uses future input. LTI causal iff h(t)=0 for t<0. Real-time systems are causal; non-causal used offline, e.g. ideal LPF.

## Answer

A **causal system** is one whose output at any time depends only on the present and past values of the input, never on future values. A **non-causal system** has an output that depends on at least one future input value.

**Causal system**
- $y(t)$ depends on $x(\tau)$ only for $\tau \le t$.
- It does not respond before the input is applied (non-anticipative).
- All physically realizable real-time systems are causal.
- Examples: $y(t) = x(t) + 2x(t-1)$; an RC circuit; $y[n] = x[n] - x[n-1]$.
- LTI condition: $h(t) = 0$ for $t < 0$ (or $h[n] = 0$ for $n < 0$).

**Non-causal system**
- The output uses future input, e.g. $y(t) = x(t+1)$, $y[n] = x[n+1] + x[n]$, $y(t) = x(-t)$.
- It cannot work in real time, but can be used when the whole signal is stored (image processing, offline audio smoothing).
- An ideal low pass filter is non-causal because its $h(t)$ is a sinc that exists for $t < 0$.

**Anti-causal system:** output depends only on present and future inputs, i.e. $h(t) = 0$ for $t > 0$.

## Check yourself

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

1. A causal system depends on:
   A. Future input
   B. Only past
   C. Present and past input only
   D. Only the future
   Answer: C. Non-anticipative. (Key point: Causal)

2. LTI causality condition:
   A. h(t)=0 for t>0
   B. h(t)=h(-t)
   C. h(0)=0
   D. h(t)=0 for t<0
   Answer: D. No response before the impulse. (Key point: LTI condition)

3. Non-causal systems are used when:
   A. The whole signal is stored, e.g. image processing
   B. Real-time processing
   C. Never
   D. Only analog circuits
   Answer: A. Offline data allows looking at future samples. (Key point: Use of non-causal)

4. Anti-causal means:
   A. Output depends only on past
   B. Output depends only on future inputs
   C. Output is zero
   D. Output is constant
   Answer: B. h(t)=0 for t>0. (Key point: Anti-causal)

## Related in Signals and Systems

- [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
- [Condition for LTI system to be causal](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Alti-causality-condition) — Signals and Systems, chapter 6, asked 3×

## Related in other subjects

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- [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
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