FOURIER SERIESEvery periodic function f(t) which has the period T 2Tt/oand has certain continuity conditions can be represented by aseries plus a constantfAt)= aa, cos (noof)b,sin (n)п %3The above holds iff(t) has a continuous derivative f'(t) forall t. It should be noted that the various sinusoids present inthe series are orthogonal on the interval 0 to T and as a resultthe coefficients are given by0(1/T)t)dta, (2/T)t) cos (nf)dt(2/T)t)sin(nwof)dt-T1,2, ...п %3DCOS1,2,..П —The constants anand bn are the Fourier coefficients of f(t) forthe interval 0 to T and the corresponding series is called theFourier series of f(t) over the same interval. SRasdeAo=3 Cosnwt ctsinsnwnusSinwsSinnwatdlACOSShws1)5nwsPEL= 3 +S6SintnussCoSsnw t6COS(SnWa 65nwoSin pwot

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Asked Nov 27, 2019
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Hi,

kindly advise if my answer is accurate or not based on the given Fourier series coefficients.

 

FOURIER SERIES
Every periodic function f(t) which has the period T 2Tt/o
and has certain continuity conditions can be represented by a
series plus a constant
fAt)= a
a, cos (noof)b,sin (n)
п %3
The above holds iff(t) has a continuous derivative f'(t) for
all t. It should be noted that the various sinusoids present in
the series are orthogonal on the interval 0 to T and as a result
the coefficients are given by
0(1/T)t)dt
a, (2/T)t) cos (nf)dt
(2/T)t)sin(nwof)dt
-T
1,2, ...
п %3D
COS
1,2,..
П —
The constants an
and bn are the Fourier coefficients of f(t) for
the interval 0 to T and the corresponding series is called the
Fourier series of f(t) over the same interval.
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FOURIER SERIES Every periodic function f(t) which has the period T 2Tt/o and has certain continuity conditions can be represented by a series plus a constant fAt)= a a, cos (noof)b,sin (n) п %3 The above holds iff(t) has a continuous derivative f'(t) for all t. It should be noted that the various sinusoids present in the series are orthogonal on the interval 0 to T and as a result the coefficients are given by 0(1/T)t)dt a, (2/T)t) cos (nf)dt (2/T)t)sin(nwof)dt -T 1,2, ... п %3D COS 1,2,.. П — The constants an and bn are the Fourier coefficients of f(t) for the interval 0 to T and the corresponding series is called the Fourier series of f(t) over the same interval.

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SRasde
Ao=
3 Cosnwt ct
sinsnw
nus
Sinws
SinnwatdlA
COSShws1)
5nws
PEL= 3 +S
6Sintnuss
CoSsnw t
6COS(SnWa 6
5nwo
Sin pwot
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SRasde Ao= 3 Cosnwt ct sinsnw nus Sinws SinnwatdlA COSShws1) 5nws PEL= 3 +S 6Sintnuss CoSsnw t 6COS(SnWa 6 5nwo Sin pwot

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Expert Answer

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Step 1

The solution for the given Fourier series problem can be obtained as follows. Compute the coefficient a0 as follows.

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For the given periodic function, observe that T =5 f(t)= 3, 0sts 5 27T 27T T 5 T 1 аo 5 3dt 5 0 3 dt x 5 5 = 3 X

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Step 2

Compute the coefficient an as follows.

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)cos()d 2 а, 0 5 2 |3 cos(пo,f) dr 6 |cos(nat)dt 11 6 sin (nat 5 по, 6 sin (5na) 5nan 2T sin 5n 5 5na 6 sin (2n 5no =0

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Step 3

Compute the coefficient bn as follows.   ...

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sin(n)dr b 11 2 [3 sin (net)dt 6 sin (na)dt cos (nert) 6 5 по, 6 Sncos(5na)-1 6 cos 5n 5no 5 6 [cos(2n7)-1 5no, 6 -[1-1 5nco 0 II

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