# 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).

find the 15th term of the geometric sequince whose first is 18 and last term of 387
I know this work
salma
The given of f(x=x-2. then what is the value of this f(3) 5f(x+1)
hmm well what is the answer
Abhi
how do they get the third part x = (32)5/4
can someone help me with some logarithmic and exponential equations.
20/(×-6^2)
Salomon
okay, so you have 6 raised to the power of 2. what is that part of your answer
I don't understand what the A with approx sign and the boxed x mean
it think it's written 20/(X-6)^2 so it's 20 divided by X-6 squared
Salomon
I'm not sure why it wrote it the other way
Salomon
I got X =-6
Salomon
ok. so take the square root of both sides, now you have plus or minus the square root of 20= x-6
oops. ignore that.
so you not have an equal sign anywhere in the original equation?
hmm
Abhi
is it a question of log
Abhi
🤔.
Abhi
I rally confuse this number And equations too I need exactly help
salma
But this is not salma it's Faiza live in lousvile Ky I garbage this so I am going collage with JCTC that the of the collage thank you my friends
salma
Commplementary angles
hello
Sherica
im all ears I need to learn
Sherica
right! what he said ⤴⤴⤴
Tamia
hii
Uday
hi
salma
what is a good calculator for all algebra; would a Casio fx 260 work with all algebra equations? please name the cheapest, thanks.
a perfect square v²+2v+_
kkk nice
algebra 2 Inequalities:If equation 2 = 0 it is an open set?
or infinite solutions?
Kim
The answer is neither. The function, 2 = 0 cannot exist. Hence, the function is undefined.
Al
y=10×
if |A| not equal to 0 and order of A is n prove that adj (adj A = |A|
rolling four fair dice and getting an even number an all four dice
Kristine 2*2*2=8
Differences Between Laspeyres and Paasche Indices
No. 7x -4y is simplified from 4x + (3y + 3x) -7y
how do you translate this in Algebraic Expressions
Need to simplify the expresin. 3/7 (x+y)-1/7 (x-1)=
. After 3 months on a diet, Lisa had lost 12% of her original weight. She lost 21 pounds. What was Lisa's original weight?
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
Yes, Nanotechnology has a very fast field of applications and their is always something new to do with it...
what is system testing
what is the application of nanotechnology?
Stotaw
In this morden time nanotechnology used in many field . 1-Electronics-manufacturad IC ,RAM,MRAM,solar panel etc 2-Helth and Medical-Nanomedicine,Drug Dilivery for cancer treatment etc 3- Atomobile -MEMS, Coating on car etc. and may other field for details you can check at Google
Azam
anybody can imagine what will be happen after 100 years from now in nano tech world
Prasenjit
after 100 year this will be not nanotechnology maybe this technology name will be change . maybe aftet 100 year . we work on electron lable practically about its properties and behaviour by the different instruments
Azam
name doesn't matter , whatever it will be change... I'm taking about effect on circumstances of the microscopic world
Prasenjit
how hard could it be to apply nanotechnology against viral infections such HIV or Ebola?
Damian
silver nanoparticles could handle the job?
Damian
not now but maybe in future only AgNP maybe any other nanomaterials
Azam
Hello
Uday
I'm interested in Nanotube
Uday
this technology will not going on for the long time , so I'm thinking about femtotechnology 10^-15
Prasenjit
can nanotechnology change the direction of the face of the world
At high concentrations (>0.01 M), the relation between absorptivity coefficient and absorbance is no longer linear. This is due to the electrostatic interactions between the quantum dots in close proximity. If the concentration of the solution is high, another effect that is seen is the scattering of light from the large number of quantum dots. This assumption only works at low concentrations of the analyte. Presence of stray light.
the Beer law works very well for dilute solutions but fails for very high concentrations. why?
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!