# Amplitude modulation (am) mathematics

 Page 1 / 1
Amplitude modulation (AM) creates interesting special effects when applied to music and speech signals. The mathematics of the modulation property of the Fourier transform are presented as the basis for understanding the AM effect, and several audio demonstrations illustrate the AM effect when applied to simple signals (sinusoids) and speech signals. The audio demonstration is implemented by a LabVIEW VI using an event structure as the basis for real-time interactive parameter control.
 This module refers to LabVIEW, a software development environment that features a graphical programming language. Please see the LabVIEW QuickStart Guide module for tutorials and documentation that will help you: •Apply LabVIEW to Audio Signal Processing •Get started with LabVIEW •Obtain a fully-functional evaluation edition of LabVIEW

## Overview

Amplitude modulation ( AM ) is normally associated with communications systems; for example, you can find all sorts of "talk radio" stations on the AM band. In communicationsystems, the baseband signal has a bandwidth similar to that of speech or music (anywhere from 8 kHz to 20 kHz), and the modulating frequency is several orders of magnitude higher; the AM radioband is 540 kHz to 1600 kHz.

When applied to audio signals for music synthesis purposes, the modulating frequency is of the same order as the audio signals to be modulated. As described below, AM (also known as ring modulation ) splits a given signal spectrum in two, and shifts one version to a higher frequency and the other version to a lower frequency. The modulated signal is the sum of the frequency-shifted spectra, and can provide interestingspecial effects when applied to speech and music signals.

## Modulation property of the fourier transform

The modulation property of the Fourier transform forms the basis of understanding how AM modifies the spectrum of a source signal. The screencast video of explains the modulation property concept and derives the equation for the modulation property.

Suppose the source signal to be modulated contains only one spectral component, i.e., the source is a sinusoid. The screencast video of shows how to apply the modulation property to predict the spectrum of the modulated signal. Once you have studied the video, try the exercises belowto ensure that you understand how to apply the property for a variety of different modulating frequencies.

The time-domain signal $x\left(t\right)$ is a sinusoid of amplitude $2A$ with corresponding frequency-domain spectrum as shown in .

Suppose $x\left(t\right)$ is modulated by a sinusoid of frequency ${f}_{m}$ . For each of the exercises below, draw the spectrum of the modulated signal $y\left(t\right)=\mathrm{cos}\left(2\pi {f}_{m}t\right)×x\left(t\right)$ , where the exercise problem statement indicates the modulation frequency.

fm = f0/5

fm = f0/2

fm = f0

fm = 1.5f0

fm = 2f0

Did you notice something interesting when ${f}_{m}$ becomes larger than ${f}_{0}$ ? The right-most negative frequency component shifts into the positive half of the spectrum, and the left-most positive frequency component shifts into the negative half of the spectrum. This effect issimilar to the idea of aliasing , in which a sinusoid whose frequency exceeds half the sampling frequency is said to be "folded back" into the principal alias. In the case of AM, modulating asinusoid by a frequency greater than its own frequency folds the left-most component back into positive frequency.

## Audio demonstrations

The screencast video of demonstrates the aural effects of modulating a single spectral component, i.e., a sinusoid.The LabVIEW code for the demo isalso described in detail, especially the use of an event structure contained in a while-loop structure (see video in ). The event structure provides an efficient way to run an algorithmwith real-time interactive parameter control without polling the front panel controls. The event structure provides an alternative to the polled method described in Real-Time Audio Output in LabVIEW .

The LabVIEW VI demonstrated within the video is available here: am_demo1.vi . Refer to TripleDisplay to install the front-panel indicator used to view the signal spectrum.

The next screencast video (see ) demonstrates the aural effects of modulating two spectral components created by summing together a sinusoid at frequency f0 and anothersinusoid at frequency 2f0. You can obtain interesting effects depending on whether the spectral components end up in a harmonic relationship; if so, the components fuse together and you perceive a singlepitch. If not, you perceive two distinct pitches.

The LabVIEW VI demonstrated within the video is available here: am_demo2.vi . Refer to TripleDisplay to install the front-panel indicator used to view the signal spectrum.

The third demonstration (see ) illustrates the effect of modulating a music clip and a speech signal. You can obtain Interesting special effectsbecause the original source spectrum simultaneously shifts to a higher and lower frequency.

The LabVIEW VI demonstrated within the video is available here: am_demo3.vi . Refer to TripleDisplay to install the front-panel indicator used to view the signal spectrum.

The two audio clips used in the example are available here: flute.wav and speech.wav (speech clip courtesy of the Open Speech Repository, www.voiptroubleshooter.com/open_speech ; the sentences are two of the many phonetically-balanced Harvard Sentences , an important standard for the speech processing community).

what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
do you think it's worthwhile in the long term to study the effects and possibilities of nanotechnology on viral treatment?
absolutely yes
Daniel
how to know photocatalytic properties of tio2 nanoparticles...what to do now
it is a goid question and i want to know the answer as well
Maciej
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
what is fullerene does it is used to make bukky balls
are you nano engineer ?
s.
fullerene is a bucky ball aka Carbon 60 molecule. It was name by the architect Fuller. He design the geodesic dome. it resembles a soccer ball.
Tarell
what is the actual application of fullerenes nowadays?
Damian
That is a great question Damian. best way to answer that question is to Google it. there are hundreds of applications for buck minister fullerenes, from medical to aerospace. you can also find plenty of research papers that will give you great detail on the potential applications of fullerenes.
Tarell
what is the Synthesis, properties,and applications of carbon nano chemistry
Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
so some one know about replacing silicon atom with phosphorous in semiconductors device?
Yeah, it is a pain to say the least. You basically have to heat the substarte up to around 1000 degrees celcius then pass phosphene gas over top of it, which is explosive and toxic by the way, under very low pressure.
Harper
Do you know which machine is used to that process?
s.
how to fabricate graphene ink ?
for screen printed electrodes ?
SUYASH
What is lattice structure?
of graphene you mean?
Ebrahim
or in general
Ebrahim
in general
s.
Graphene has a hexagonal structure
tahir
On having this app for quite a bit time, Haven't realised there's a chat room in it.
Cied
what is biological synthesis of nanoparticles
what's the easiest and fastest way to the synthesize AgNP?
China
Cied
types of nano material
I start with an easy one. carbon nanotubes woven into a long filament like a string
Porter
many many of nanotubes
Porter
what is the k.e before it land
Yasmin
what is the function of carbon nanotubes?
Cesar
I'm interested in nanotube
Uday
what is nanomaterials​ and their applications of sensors.
what is nano technology
what is system testing?
preparation of nanomaterial
how did you get the value of 2000N.What calculations are needed to arrive at it
Privacy Information Security Software Version 1.1a
Good
Got questions? Join the online conversation and get instant answers!