# 6.1 Lab 5: theory

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This module introduces frequency shift keying (FSK) and describes components of an FSK transmitter block-diagram.

## Frequency shift keying

Frequency Shift Keying ( FSK ) is a scheme to transmit digital information across an analogchannel. Binary data bits are grouped into blocks of a fixed size, and each block is represented by a unique carrierfrequency, called a symbol , to be sent across the channel.

The receiver then looks at the recovered symbol frequency to determine which block of bitswas sent and converts it back to the appropriate binary data.
This requires having a unique symbol for each possible combination of data bits in a block. In thislaboratory exercise each symbol represents a two-bit block; therefore, there will be four different symbols.

The carrier frequency is kept constant over some number of samples known as the symbol period( ${T}_{\mathrm{symb}}$ ). The symbol rate, defined as ${F}_{\mathrm{symb}}$ , is a fraction of the board's sampling rate, ${F}_{s}$ . For our sampling rate of 44.1 kHz and a symbol period of 32, the symbol rate is 44.1k/32 symbols per second.

## Pseudo-noise sequence generator

The input bits to the transmitter are provided by the special shift-register, called a pseudo-noise sequence generator ( PN generator ), on the left side of . A PN generator produces a sequence of bits that appears random. The PN sequence will repeat withperiod $2^{B}-1$ , where $B$ is the width in bits of the shift register. A more detailed diagram of the PN generator alone appears in .

As shown in , the PN generator is simply a shift-register and XOR gate. Bits 14 and 15 of theshift-register are XORed together and the result is shifted into the lowest bit of the register. This lowest bit isthe output of the PN generator.

The PN generator is a useful source of random data bits for system testing. We can simulate the bit sequence that wouldbe transmitted by a user as the random bits generated by the PN generator. Since communication systems tend to randomizethe bits seen by the transmission scheme so that bandwidth can be efficiently utilized, the PN generator is a good datamodel.

PN generators have other applications in communications, notably in the Code DivisionMultiple Access schemes used by cellular telephones.

## Series-to-parallel conversion

The shift-register produces one output bit at a time. Because each symbol the system transmits will encode two bits, werequire the series-to-parallel conversion to group the output bits from the shift-register into blocks of two bits so thatthey can be mapped to a symbol.

## Frequency look-up table

This is responsible for mapping blocks of bits to one of four frequencies as shown in . Each possible two-bit block of data from the series-to-parallel conversionis mapped to a different carrier frequency ${}_{i}$

Note that the subscript $i$ denotes a symbol's index in the transmitted signal; i.e. , the first symbol sent has index $i=1$ , the second symbol sent has index $i=2$ , and so on. Therefore, ${}_{i}$ denotes the frequency and ${}_{i}$ denotes the phase offset of the ${i}^{\mathrm{th}}$ transmitted symbol.
These frequencies are then used to generate the waveforms. The mappings for thisassignment are given in .

Data Chunk Carrier Frequency ${}_{i}$
00 $\frac{9\pi }{32}$
01 $\frac{13\pi }{32}$
11 $\frac{17\pi }{32}$
10 $\frac{21\pi }{32}$

One way to implement this mapping is by using a look-up table. The two-bit data block can be interpreted as an offsetinto a frequency table where we have stored the possible transmission frequencies. Note that since each frequencymapping defines a symbol, this mapping is done at the symbol rate ${F}_{\mathrm{symb}}$ , or once for every ${T}_{\mathrm{symb}}$ DSP samples.

The symbol bit assignments are such that any two adjacent frequencies map to data blocks that differ by only one bit.This assignment is called Gray coding and helps reduce the number of bit errors made in the event of areceived symbol error.

## Phase continuity

In order to minimize the bandwidth used by the transmitted signal, you should ensure that the phase of your transmittedwaveform is continuous between symbols; i.e., the beginning phase of any symbol must be equal to the ending phase of theprevious symbol. For instance, if a symbol of frequency $\frac{9\pi }{32}$ begins at phase 0, the symbol will end 31 output samples later at phase $31\frac{9\pi }{32}$ . To preserve phase continuity, the next output sample must be at phase $32\frac{9\pi }{32}$ , which is equivalent to phase $\pi$ . Therefore, the next symbol, whatever its frequency, must begin at phase $\pi$ . For each symbol, you must choose ${}_{i}$ in the expression $\sin ({}_{i}n+{}_{i})$ to create this continuity.

#### Questions & Answers

Is there any normative that regulates the use of silver nanoparticles?
Damian Reply
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Renato
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research.net
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Introduction about quantum dots in nanotechnology
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there is no specific books for beginners but there is book called principle of nanotechnology
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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
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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.
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CYNTHIA
carbon nanotubes has various application in fuel cells membrane, current research on cancer drug,and in electronics MEMS and NEMS etc
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s. Reply
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of graphene you mean?
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or in general
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in general
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Graphene has a hexagonal structure
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