---
title: "Why band-limit a signal before sampling"
subject: "Data Communication"
chapter: 5
key: "semester_5/data_communication:sampling-bandlimit"
source: https://www.bctengineer.com/q/semester_5/data_communication/sampling-bandlimit
site: BCT Engineering
---

# Why band-limit a signal before sampling

Data Communication · Chapter 5: Data Encoding and Modulation

- Asked in: 2069 Asar, 2 marks
- Video: [The intuition behind the Nyquist-Shannon Sampling Theorem](https://www.youtube.com/watch?v=Jv5FU8oUWEY) — Zach Star
- Answer checked by Claude Sonnet 5.5 on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_5/data_communication/sampling-bandlimit
- Whole chapter: https://www.bctengineer.com/md/semester_5/data_communication/chapter-5

## Question

Why is it necessary to limit the band of a signal before performing sampling?

## Short answer

To prevent aliasing, where frequency components above half the sampling rate fold into the baseband and corrupt the signal, a low-pass anti-aliasing filter must limit the signal band below the Nyquist frequency. This ensures the sampling theorem condition fs ≥ 2fmax is satisfied.

## Answer

Sampling a signal at rate *fs* repeats its spectrum around every multiple of *fs*. If the signal has frequency components above *fs*/2, the repeated spectra overlap and the original signal cannot be recovered. This distortion is called **aliasing**.

- Nyquist theorem: no aliasing only if *fs* ≥ 2 *fmax*.
- Real signals (speech, noise) contain components well above the band of interest, and *fs* cannot be made infinite.
- So the signal is first passed through a **low-pass anti-aliasing filter** that removes everything above *fs*/2. The signal is then truly band-limited and the sampling theorem holds.

Example: a telephone voice channel is filtered to about 4 kHz before sampling at 8000 samples/s. Without the filter, 6 kHz noise would alias to 2 kHz and appear as false audio in the speech.

## Check yourself

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

1. What happens if components above fs/2 are present when sampling?
   A. The signal is amplified
   B. Repeated spectra overlap (aliasing) and the signal cannot be recovered
   C. The sampling rate doubles
   D. Nothing; they are ignored
   Answer: B. Spectrum copies around multiples of fs overlap, causing aliasing. (Key point: Aliasing)

2. What filter is used before sampling?
   A. High-pass
   B. Band-stop
   C. Low-pass removing everything above fs/2
   D. All-pass
   Answer: C. A low-pass anti-aliasing filter band-limits the signal so the sampling theorem holds. (Key point: Anti-aliasing filter)

3. A voice channel filtered to about 4 kHz is sampled at 8000/s. Without the filter, 6 kHz noise would appear as?
   A. 6 kHz
   B. 2 kHz false audio
   C. 10 kHz
   D. No effect
   Answer: B. 8000 - 6000 = 2 kHz alias. (Key point: Example)

## Related in other subjects

- [Practical sampling; band-pass sampling](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Apractical-bandpass-sampling) — Signals and Systems, chapter 4
- [Aliasing in a band-limited signal](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Aaliasing-bandlimited-w) — Signals and Systems, chapter 4
- [Quantization, rounding vs truncation, dead band](https://www.bctengineer.com/question.md?key=semester_7%2Fdigital_signal_analysis_and_processing%3Aquantization-rounding-limit-dead-band) — Digital Signal Analysis and Processing, chapter 4
- [Delta modulator numerical (3 kHz, 10 kHz sampling)](https://www.bctengineer.com/question.md?key=semester_6%2Fcommunication_systems%3Adm-3khz-10khz-numerical) — Communication Systems, chapter 4, asked 2×