# 6.14 Frequency shift keying

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Frequency Shift Keying uses the bit to affect the frequency of a carrier sinusoid.

In frequency-shift keying (FSK), the bit affects the frequency of a carrier sinusoid.

${s}_{0}(t)=A{p}_{T}(t)\sin (2\pi {f}_{0}t)$
${s}_{1}(t)=A{p}_{T}(t)\sin (2\pi {f}_{1}t)$

The frequencies ${f}_{0}$ , ${f}_{1}$ are usually harmonically related to the bit interval. In the depicted example, ${f}_{0}=\frac{3}{T}$ and ${f}_{1}=\frac{4}{T}$ . As can be seen from the transmitted signal for our example bit stream ( [link] ), the transitions at bit interval boundaries are smoother than thoseof BPSK . This plot shows the FSK waveform for same bitstream used in the BPSK example .

To determine the bandwidth required by this signal set, we again consider the alternating bit stream. Think of it as two signalsadded together: The first comprised of the signal ${s}_{0}(t)$ , the zero signal, ${s}_{0}(t)$ , zero, etc. , and the second having the same structure but interleaved with the first and containing ${s}_{1}(t)$ ( [link] ). The depicted decomposition of the FSK-modulated alternating bit stream into its frequency components simplifies thecalculation of its bandwidth.

Each component can be thought of as a fixed-frequency sinusoid multiplied by a square wave of period $2T$ that alternates between one and zero. This baseband square wave has the same Fourier spectrum as our BPSK example, but with theaddition of the constant term ${c}_{0}$ . This quantity's presence changes the number of Fourier series terms required for the 90% bandwidth: Now we needonly include the zero and first harmonics to achieve it. The bandwidth thus equals, with ${f}_{0}< {f}_{1}$ , ${f}_{1}+\frac{1}{2T}-{f}_{0}-\frac{1}{2T}={f}_{1}-{f}_{0}+\frac{1}{T}$ . If the two frequencies are harmonics of the bit-interval duration, ${f}_{0}=\frac{{k}_{0}}{T}$ and ${f}_{1}=\frac{{k}_{1}}{T}$ with ${k}_{1}> {k}_{0}$ , the bandwidth equals $\frac{{k}_{1}+-{k}_{0}+1}{T}$ . If the difference between harmonic numbers is $1$ , then the FSK bandwidth is smaller than the BPSK bandwidth. If the difference is $2$ , the bandwidths are equal and larger differences produce a transmission bandwidthlarger than that resulting from using a BPSK signal set.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
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Renato
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?
Kyle
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why?
what school?
Kyle
biomolecules are e building blocks of every organics and inorganic materials.
Joe
anyone know any internet site where one can find nanotechnology papers?
research.net
kanaga
sciencedirect big data base
Ernesto
Introduction about quantum dots in nanotechnology
what does nano mean?
nano basically means 10^(-9). nanometer is a unit to measure length.
Bharti
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absolutely yes
Daniel
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it is a goid question and i want to know the answer as well
Maciej
characteristics of micro business
Abigail
for teaching engĺish at school how nano technology help us
Anassong
Do somebody tell me a best nano engineering book for beginners?
there is no specific books for beginners but there is book called principle of nanotechnology
NANO
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
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Mostly, they use nano carbon for electronics and for materials to be strengthened.
Virgil
is Bucky paper clear?
CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
NANO
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
how did you get the value of 2000N.What calculations are needed to arrive at it
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