- Trending Categories
- Data Structure
- Networking
- RDBMS
- Operating System
- Java
- iOS
- HTML
- CSS
- Android
- Python
- C Programming
- C++
- C#
- MongoDB
- MySQL
- Javascript
- PHP

- Selected Reading
- UPSC IAS Exams Notes
- Developer's Best Practices
- Questions and Answers
- Effective Resume Writing
- HR Interview Questions
- Computer Glossary
- Who is Who

# Effects of Undersampling (Aliasing) and Anti-Aliasing Filter

## What is Sampling?

The process of converting a continuous-time signal into a discrete-time signal is called *sampling*. Once the sampling is done, the signal is defined at discrete instants of time and the time interval between two successive sampling instants is called the *sampling period.*

## Nyquist Rate of Sampling

The Nyquist rate of sampling is the theoretical minimum sampling rate at which a signal can be sampled and still be reconstructed from its samples without any distortion.

## Effects of Under Sampling (Aliasing)

If a signal is sampled at less than its Nyquist rate, then it is called **undersampled.**

The spectrum of the sampled signal is given by,

$$\mathrm{\mathit{X_{s}\mathrm{\left(\omega \right )}\:\mathrm{=}\:\frac{\mathrm{1}}{\mathit{T}}\sum_{n\mathrm{=-\infty }}^{\infty }\mathit{X\mathrm{\left ( \mathit{\omega -n\omega _{s}} \right )}}}}$$

When a signal is undersampled, i.e.,$\mathrm{\left ( \mathit{\omega _{s}<\mathrm{2}\omega _{m}} \right )}$ where, $\mathit{\omega _{s}}$ is the sampling frequency and $\mathit{\omega _{m}}$ is the maximum frequency component present in the signal. Then, the frequency spectrum $\mathit{X\mathrm{\left ( \omega \right )}}$ of the signal $\mathit{x\mathrm{\left ( \mathit{t}\right )}}$ is no longer replicated in the spectrum of the sampled signal $\mathrm{\left[\mathit{X_{s}}\mathrm{\left (\omega \right )} \right ]}$ and hence it cannot be reconstructed by a low-pass filter. Thus, the effect in which the individual terms in the equation of $\mathit{X_{s}\mathrm{\left ( \omega \right )}}$ overlap is said to be aliasing. This process of spectral overlap is also known as **frequency folding effect.**

Therefore, the phenomenon in which a high-frequency component in the frequency spectrum of signal takes identity of a lower frequency component in the spectrum of the sampled signal is called **aliasing**.

Aliasing can occur if any of the following conditions exists −

The sampling rate is very low.

The signal is not band-limited to a finite range.

In order to avoid aliasing, it should be ensured that −

$\mathit{\omega _{s}}$ is greater than $2\mathit{\omega _{m}}$.

The signal $\mathit{x\mathrm{\left ( \mathit{t}\right )}}$ must be band-limited.

## Anti-Aliasing Filter

The low-pass filter that is used for band-limiting a signal before sampling is called the **anti-aliasing filter.**

As the sampling theorem states that a signal can be perfectly reconstructed from its samples only when it is band-limited. But, in practice, no signal is completely band-limited, i.e., the signals have frequency spectra consisting of low-frequency components together with high-frequency noise components.

When a signal is sampled with sampling frequency ${\mathrm{\left ( \mathit{\omega _{s}} \right )}}$, then all the signals with frequency range higher than $\mathrm{\left(\mathit{\omega _{s}/\mathrm{2}} \right )}$ creating aliasing. Thus, in order to avoiding the aliasing errors caused by the undesired high-frequency signals, it is necessary to first band-limit the signal $\mathit{x\mathrm{\left ( \mathit{t} \right )}}$ to some appropriate frequency $\mathit{\omega _{m}}$ by using the low-pass filter such that most of the energy of the signal is retained. This low-pass filter (LPF) is commonly known as the *anti-aliasing
filter.*

- Related Questions & Answers
- Aliasing in PostgreSQL?
- PHP Aliasing/Importing namespaces
- Why strict aliasing is required in C?
- Working with CSS3 Filter Effects
- Difference between Firewall and Anti-virus
- Credit Monitoring Services and Other Anti-Fraud Protection
- Signals and Systems: Causal, Non-Causal, and Anti-Causal Signals
- Anti Clockwise spiral traversal of a binary tree?
- Filter array with filter() and includes() in JavaScript
- What are the Effects of Cyberwarfare?
- Hunting in Synchronous Motor – Causes, Effects and Reduction of Hunting
- What is anaemia and what are its effects?
- What is Osteoporosis and what are its effects?
- Top Free Anti – Virus Softwares
- Bypass Anti-virus using Veil Framework