# 4.4 Aliasing applet

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Applet demonstrating the concept of aliasing

The applet is courtesy of the Digital Signal Processing tutorial at freeuk.com, http://www.dsptutor.freeuk.com/ . You can also have a look at the Light Wheel applet .

## Introduction

In this module we shall look at sampling a sinusoidal signal. According to the sampling theorem , a sinusoidal signal can be exactly reconstructed from values sampled atdiscrete, uniform intervals as long as the signal frequency is less than half the sampling frequency. Any component of a sampled signal with a frequency above thislimit, often referred to as the folding frequency, is subject to aliasing .

The applet is based on a fixed sampling rate of ${F}_{s}=8000 samples per second$ (one sample every 0.125 milliseconds, i.e ${T}_{s}=\frac{1}{8000}$ ).

## Instructions

Set the frequency of the sinusoidal signal, in Hz, in the "Input frequency" box, i.e choose an $f$ in the following signal: $\sin (2\pi ft)$ . When you click the "Plot" button, with "Input signal" checked, the input signal is plotted againsttime.

The "Grid" checkbox toggles on and off vertical gridlines indicating the instants at which the signal is sampled.The "Sample points", representing the sampled values of the input signal, can also be toggled.

Finally, the "Alias frequency" checkbox (visible only when aliasing occurs) controls the plotting of the "reconstructed" sinusoidal signal, with $f={f}_{\mathrm{alias}}$ .

## Overview of the process

When using the applet it is important to have an understanding of where the different signals occurin a sampling system.

Relating the applet signals to the figure we get
• Input signal = $x(t)=\sin (2\pi ft)$ , where $f$ is the input frequency chosen by the user.
• The sampled signal = ${x}_{s}(n)=\sin (2\pi fn{T}_{s})=\sin (2\pi fn\frac{1}{8000})$ .
• The reconstructed signal = $\stackrel{}{x}(\mathrm{\left(t\right)})$ , is shown as the original signalif sampling is done fast enough, or as the aliased signal if sampling is too slow.
( $h(t)$ is an ideal reconstruction filter).

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