---
title: "What is aliasing; how to prevent it"
subject: "Signals and Systems"
chapter: 4
key: "semester_4/signals_and_systems:aliasing-prevention"
source: https://www.bctengineer.com/q/semester_4/signals_and_systems/aliasing-prevention
site: BCT Engineering
---

# What is aliasing; how to prevent it

Signals and Systems · Chapter 4: Sampling

- Asked in: 2079 Asoj, 6 marks; 2079 Chaitra, 6 marks (asked 2 times)
- Video: [Aliasing or Effect of Under Sampling | Generation of Aliasing | Effect and Solution of Aliasing](https://www.youtube.com/watch?v=lT8wKrLfcFU) — Engineering Funda
- Answer checked by Claude Opus 5.5 (high effort) on 2026-10-14
- Page: https://www.bctengineer.com/q/semester_4/signals_and_systems/aliasing-prevention
- Whole chapter: https://www.bctengineer.com/md/semester_4/signals_and_systems/chapter-4

## Question

What is aliasing and how can it be prevented?

## Short answer

Aliasing is the distortion from sampling below twice the highest frequency; spectral copies overlap and high frequencies fold into lower false frequencies. Prevent it by sampling above the Nyquist rate, using an anti-aliasing low-pass filter with cutoff fs/2 before sampling, and leaving a guard band or oversampling.

## Answer

**Aliasing** is the distortion that occurs when a signal is sampled at a rate lower than twice its highest frequency ($f_s < 2f_m$). The shifted copies of the spectrum overlap, so high-frequency components fold back and appear as lower frequencies. After this, the original signal cannot be recovered by any filter.

#### Why it happens

Sampling with an impulse train of rate $f_s$ makes the spectrum periodic:

$$
X_s(f) = f_s\sum_{k=-\infty}^{\infty}X(f - kf_s)
$$

Each copy occupies $kf_s - f_m$ to $kf_s + f_m$. The copies are separate only if $f_s - f_m \ge f_m$, i.e. $f_s \ge 2f_m$.

```text
 fs > 2fm (no aliasing):
   ___       ___       ___
  /   \     /   \     /   \
-+--+--+---+--+--+---+--+--+--> f
  -fm 0 fm    fs        2fs

 fs < 2fm (aliasing: tails overlap):
   ____ ____ ____
  /    X    X    \
-+---+----+----+---> f
     0    fs   2fs
```

**Example:** A 700 Hz tone sampled at 1000 Hz gives samples identical to a 300 Hz tone ($|700 - 1000| = 300$ Hz). The 700 Hz tone has been "aliased" to 300 Hz.

#### Effects

- False frequencies appear in the reconstructed signal.
- In images, aliasing causes jagged edges and moiré patterns; in video, wheels seem to turn backwards.

#### Prevention

1. **Sample above the Nyquist rate:** choose $f_s > 2f_m$, usually with a margin (e.g. CD audio uses 44.1 kHz for a 20 kHz band).
2. **Anti-aliasing (pre-)filter:** pass the analog signal through a low-pass filter with cutoff $f_s/2$ before the sampler. Real signals are never perfectly band-limited, and noise has high frequencies; the filter removes these before they can fold back.
3. **Guard band:** since practical filters are not ideal, keep $f_s$ comfortably above $2f_m$ so that the filter's transition band fits between $f_m$ and $f_s - f_m$.
4. **Oversampling:** sample at a much higher rate, then filter and decimate digitally; this relaxes the analog filter requirement.

```text
x(t) -> [Anti-aliasing LPF, fc = fs/2] -> [Sampler fs] -> [ADC]
```

## Check yourself

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

1. What does impulse sampling do to the spectrum?
   A. Shifts it once to fs
   B. Narrows its bandwidth
   C. Makes it periodic: copies repeat every fs
   D. Multiplies it by a sinc
   Answer: C. X_s(f) = fs * sum X(f - k fs). (Key point: Spectrum of sampled signal)

2. Copies stay separate when
   A. fs <= fm
   B. fs - fm <= fm
   C. fs = fm
   D. fs - fm >= fm, i.e. fs >= 2fm
   Answer: D. The first copy starts at fs - fm, which must not go below fm. (Key point: No-overlap condition)

3. A 700 Hz tone sampled at 1000 Hz appears as
   A. 300 Hz
   B. 700 Hz
   C. 1700 Hz
   D. 1000 Hz
   Answer: A. |700 - 1000| = 300 Hz. (Key point: Example)

4. Where is the anti-aliasing filter placed and what is its cutoff?
   A. After the sampler, high-pass at fs
   B. Before the sampler, low-pass with cutoff fs/2
   C. After the DAC, low-pass at 2fs
   D. Before the sampler, high-pass at fs/2
   Answer: B. It removes components above fs/2 before they can fold back. (Key point: Anti-aliasing filter)

## Related in Signals and Systems

- [How Nyquist criterion prevents aliasing](https://www.bctengineer.com/question.md?key=semester_4%2Fsignals_and_systems%3Anyquist-prevents-aliasing) — Signals and Systems, chapter 4