# 0.4 Analog (de)modulation  (Page 6/9)

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TRUE or FALSE: A small, fixed phase offset in the receiver demodulatingAM with suppressed carrier produces an undesirable low frequency modulated version of the analog message.

Try different frequency offsets gam $=$ $\left[.014$ , $0.1$ , $1.0$ , $10\right]$ . 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 $m\left(t\right)$ ? Hint: look over more than just the first $1/10$ second to see the effect.

Consider the system shown in [link] . Show that the output of the system is $2{A}_{0}w\left(t\right)cos\left(2\pi {f}_{c}t\right)$ , as indicated.

Create a M atlab routine to implement the square-law mixing modulator of [link] .

1. Create a signal $w\left(t\right)$ that has bandwidth 100 Hz
2. Modulate the signal to 1000 Hz.
3. Demodulate using the AM demodulator from AM.m (to recover the original $w\left(t\right)$ ).

Exercise [link] essentially creates a transmitter and receiver based on the square-law modulator(rather than the more standard mixing modulator). Using this system:

1. Show how the received signal degrades if the phase of the cosine wave is not known exactly.
2. Show how the received signal degrades if the frequency of the cosine wave is not exact.
3. Show how the received signal degrades if the bandpass filter is not centered at the specified frequency.

Consider the transmission system of [link] . The message signal $w\left(t\right)$ has magnitude spectrum shown in part (a).The transmitter in part (b) produces the transmitted signal $x\left(t\right)$ which passes through the channel in part (c). The channel scales thesignal and adds narrowband interferers to create the received signal $r\left(t\right)$ . The transmitter and channel parameters are ${\Phi }_{1}=0.3$ radians, ${f}_{1}=24.1$ kHz, ${f}_{2}=23.9$ kHz, ${f}_{3}=27.5$ kHz, ${f}_{4}=29.3$ kHz, and ${f}_{5}=22.6$ kHz. Thereceiver processing $r\left(t\right)$ is shown in [link] (d). All bandpass and lowpass filters are considered ideal with a gainof unity in the passband and zero in the stopband.

1. Sketch $|R\left(f\right)|$ for $-30$ kHz $\le f\le$ 30kHz. Clearly indicate the amplitudes and frequencies of key points in the sketch.
2. Assume that ${\Phi }_{2}$ is chosen to maximize the magnitude of $y\left(t\right)$ and reflects the value of ${\Phi }_{1}$ and the delays imposed by the two ideal bandpass filters that form thereceived signal $r\left(t\right)$ . Select the receiver parameters ${f}_{6}$ , ${f}_{7}$ , ${f}_{8}$ , and ${f}_{9}$ , so the receiver output $y\left(t\right)$ is a scaled version of $w\left(t\right)$ .

An analog baseband message signal $w\left(t\right)$ has all energy between $-B$ and $B$ Hz. It is upconverted to the transmitted passband signal $x\left(t\right)$ via AM with suppressed carrier

$x\left(t\right)=w\left(t\right)cos\left(2\pi {f}_{c}t+{\Phi }_{c}\right)$

where a carrier frequency ${f}_{c}>10B$ . The channel is a pure delay and the received signal $r$ is $r\left(t\right)=x\left(t-d\right)$ where the delay $d=n{T}_{c}+{T}_{c}/\alpha$ is an integer multiple $n\ge 0$ of the carrier period ${T}_{c}$ ( $=1/{f}_{c}$ ) plus a fraction of ${T}_{c}$ given by $\alpha >1$ . The mixer at the receiver is perfectly synchronizedto the transmitter so that the mixer output $y\left(t\right)$ is

$y\left(t\right)=r\left(t\right)cos\left(2\pi {f}_{c}t+{\Phi }_{r}\right).$

The receiver mixer phase may not match the transmitter mixer phase ${\Phi }_{c}$ . The receiver lowpass filters $y$ to produce

$v\left(t\right)=\mathrm{LPF}\left\{y\left(t\right)\right\}$

where the lowpass filter is ideal with unity passband gain, linear passband phase with zero phase at zero frequency, and cutoff frequency $1.2B$ .

1. Write a formula for the receiver mixer output $y\left(t\right)$ as a function of ${f}_{c}$ , ${\Phi }_{c}$ , $d$ , $\alpha$ , ${\Phi }_{r}$ , and $w\left(t\right)$ (without use of $x$ , $r$ , $n$ , or ${T}_{c}$ ).
2. Determine the amplitude of the minimum and maximum values of $y\left(t\right)$ for $\alpha =4$ .
3. For $\alpha =6$ , $n=42$ , ${\Phi }_{c}=0.2$ radians, and ${T}_{c}=20\phantom{\rule{4pt}{0ex}}\mu$ sec, determine ${\Phi }_{r}$ that maximizes the magnitude of the maximum and minimum values of $v\left(t\right)$ .

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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