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 Course: Research Note Topic: Research Note Description: Consider the 0 and 1 step function f(x) as shown in my seminar description above. We compute the Fourier series as follows.

f(x)= 0     0     =  1     pi/2f(x)= ao/2+summation an cosnwx+summation bn sinnwx

w=2pi/T where T is time

T=pi

Therefore w=2pi/pi

=2

ie time taken by 0 and 1

w=frequency

ao =2/T( (integration 0 dx limit 0 to pi/2)+ (integration 1 dx limit pi/2 to pi))

=2/pi(pi-pi/2)limit pi/2 to pi

=1

an=2/T ((integration 0 cos2nx dx limit 0 to pi/2)+( integration 1 cos2nx dx limit pi/2 to pi))

=2/pi (sin2nx limit pi/2 to pi)

=2/pi2n(sin2npi-sinnpi)

sin2npi=0 sin npi=0

=0

bn=2/T((integration 0 sin2nx dx limit 0 to pi/2)+(integration  1 sin2nx dx limit pi/2 to pi))

=2/pi n(-cos2nx limit pi/2 to pi))

=1/npi(-cos2npi+cosnpi)

cos npi=(-1)power n

cos 2npi=1

=1/n pi (-1+(-1)power n)

bn=if n=1,3,5 ie odd

= -2/pi(sin 2 pi+ sin 6 pi/3 + sin 10 pi/5 . . . . .

f(x)= 1/2 – 2/pi ( sin 2 pi+ sin 6 pi/3 + sin 10 pi/5 . . . . . . . . infinity

now the function f(x)  which is determined by the Fourier series will overlap the digital function f(x)  as shown in above graph and it will superpose it. Thus the digital  signal is converted into sinusoidal electrical signal and data is send from one computer to the other by electrical cables. Your Password: