# 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).

how can chip be made from sand
is this allso about nanoscale material
Almas
are nano particles real
yeah
Joseph
Hello, if I study Physics teacher in bachelor, can I study Nanotechnology in master?
no can't
Lohitha
where is the latest information on a no technology how can I find it
William
currently
William
where we get a research paper on Nano chemistry....?
nanopartical of organic/inorganic / physical chemistry , pdf / thesis / review
Ali
what are the products of Nano chemistry?
There are lots of products of nano chemistry... Like nano coatings.....carbon fiber.. And lots of others..
learn
Even nanotechnology is pretty much all about chemistry... Its the chemistry on quantum or atomic level
learn
da
no nanotechnology is also a part of physics and maths it requires angle formulas and some pressure regarding concepts
Bhagvanji
hey
Giriraj
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
has a lot of application modern world
Kamaluddeen
yes
narayan
what is variations in raman spectra for nanomaterials
ya I also want to know the raman spectra
Bhagvanji
I only see partial conversation and what's the question here!
what about nanotechnology for water purification
please someone correct me if I'm wrong but I think one can use nanoparticles, specially silver nanoparticles for water treatment.
Damian
yes that's correct
Professor
I think
Professor
Nasa has use it in the 60's, copper as water purification in the moon travel.
Alexandre
nanocopper obvius
Alexandre
what is the stm
is there industrial application of fullrenes. What is the method to prepare fullrene on large scale.?
Rafiq
industrial application...? mmm I think on the medical side as drug carrier, but you should go deeper on your research, I may be wrong
Damian
How we are making nano material?
what is a peer
What is meant by 'nano scale'?
What is STMs full form?
LITNING
scanning tunneling microscope
Sahil
how nano science is used for hydrophobicity
Santosh
Do u think that Graphene and Fullrene fiber can be used to make Air Plane body structure the lightest and strongest. Rafiq
Rafiq
what is differents between GO and RGO?
Mahi
what is simplest way to understand the applications of nano robots used to detect the cancer affected cell of human body.? How this robot is carried to required site of body cell.? what will be the carrier material and how can be detected that correct delivery of drug is done Rafiq
Rafiq
if virus is killing to make ARTIFICIAL DNA OF GRAPHENE FOR KILLED THE VIRUS .THIS IS OUR ASSUMPTION
Anam
analytical skills graphene is prepared to kill any type viruses .
Anam
Any one who tell me about Preparation and application of Nanomaterial for drug Delivery
Hafiz
what is Nano technology ?
write examples of Nano molecule?
Bob
The nanotechnology is as new science, to scale nanometric
brayan
nanotechnology is the study, desing, synthesis, manipulation and application of materials and functional systems through control of matter at nanoscale
Damian
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!