# 0.4 Analog (de)modulation  (Page 5/9)

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To continue the investigation, suppose that the carrier phase offset is zero, (i.e.,  $\Phi =0$ ), but that the frequency offset $\gamma$ is not. Then the spectrum of $x\left(t\right)$ from [link] is

$\begin{array}{ccc}\hfill X\left(f\right)=\frac{{A}_{c}}{4}\left[W\left(f-\gamma \right)& +& W\left(f-2{f}_{c}-\gamma \right)\hfill \\ & +& W\left(f+2{f}_{c}+\gamma \right)+W\left(f+\gamma \right)\right],\hfill \end{array}$

and the lowpass filtering of $x\left(t\right)$ produces

$M\left(f\right)=\frac{{A}_{c}}{4}\left[W,\left(,f,-,\gamma ,\right),+,W,\left(,f,+,\gamma ,\right)\right].$

This is shown in [link] . Recognizing this spectrum as a frequency shiftedversion of $w\left(t\right)$ , it can be translated back into the time domain using [link] to give

$m\left(t\right)=\frac{{A}_{c}}{2}w\left(t\right)\phantom{\rule{4pt}{0ex}}\mathrm{cos}\left(2\pi \gamma t\right).$

Instead of recovering the message $w\left(t\right)$ , the frequency offset causes the receiver to recover a low frequencyamplitude modulated version of it. This is bad with even a small carrier frequency offset.While $\mathrm{cos}\left(\Phi \right)$ in [link] is a fixed scaling, $\mathrm{cos}\left(2\pi \gamma t\right)$ in [link] is a time-varying scaling that will alternately recover $m\left(t\right)$ (when $\mathrm{cos}\left(2\pi \gamma t\right)\approx 1$ ) and make recovery impossible (when $\mathrm{cos}\left(2\pi \gamma t\right)\approx 0$ ). Transmitters are typically expected to maintain suitableaccuracy to a nominal carrier frequency setting known to the receiver. Ways of automatically tracking (inevitable) smallfrequency deviations are discussed at length in [link] .

The following code AM.m generates a message $w\left(t\right)$ and modulates it with a carrier at frequency ${f}_{c}$ . The demodulation is done with a cosine offrequency ${f}_{c}+\gamma$ and a phase offset of $\Phi$ . When $\gamma =0$ and $\Phi =0$ , the output (a lowpass version of the demodulated signal)is nearly identical to the original message, except for the inevitable delay caused by the linearfilter. [link] shows four plots: the message $w\left(t\right)$ on top, followed by the upconverted signal $v\left(t\right)=w\left(t\right)cos\left(2\pi {f}_{c}t\right)$ , followed in turn by the downconverted signal $x\left(t\right)$ . The lowpass filtered versionis shown in the bottom plot; observe that it is nearly identical to the original message, albeit with a slight delay.

time=.3; Ts=1/10000;                        % sampling interval and time base t=Ts:Ts:time; lent=length(t);               % define a "time" vectorfc=1000; c=cos(2*pi*fc*t);                  % define the carrier at freq fc fm=20; w=5/lent*(1:lent)+cos(2*pi*fm*t);    % create "message"v=c.*w;                                     % modulate with carrier gam=0; phi=0;                               % freq & phase offset c2=cos(2*pi*(fc+gam)*t+phi);                % create cosine for demodx=v.*c2;                                    % demod received signal fbe=[0 0.1 0.2 1]; damps=[1 1 0 0]; fl=100;  % low pass filter designb=firpm(fl,fbe,damps);                      % impulse response of LPF m=2*filter(b,1,x);                          % LPF the demodulated signal AM.m suppressed carrier with (possible) freq and phase offset (download file) 

Using AM.m as a starting point, plot the spectra of $w\left(t\right)$ , $v\left(t\right)$ , $x\left(t\right)$ , and $m\left(t\right)$ .

Try different phase offsets $\Phi$ $=$ $\left[-\pi$ , $-\pi /2$ , $-\pi /3$ , $-\pi /6$ , 0, $\pi /6$ , $\pi /3$ , $\pi /2$ , $\pi \right]$ . How well does the recovered message $m\left(t\right)$ match the actual message $w\left(t\right)$ ? For each case, what is the spectrum of $m\left(t\right)$ ?

where we get a research paper on Nano chemistry....?
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
Preparation and Applications of Nanomaterial for Drug Delivery
revolt
da
Application of nanotechnology in medicine
what is variations in raman spectra for nanomaterials
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
Is there any normative that regulates the use of silver nanoparticles?
what king of growth are you checking .?
Renato
What fields keep nano created devices from performing or assimulating ? Magnetic fields ? Are do they assimilate ?
why we need to study biomolecules, molecular biology in nanotechnology?
?
Kyle
yes I'm doing my masters in nanotechnology, we are being studying all these domains as well..
why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
how did you get the value of 2000N.What calculations are needed to arrive at it
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