S 17B.1
______
Using 2*cos(theta) = exp(j*theta) + exp(j*theta), we see that
s(t) can be expressed as the (unweighted) sum of eight complex
sinusoids of the form
exp(2*pi*f*t) ,
where f (Hz) takes the four positive values (in Hz)
23+25+30 = 78
23+2530 = 18
23+25+30 = 32
2325+30 = 28 ,
as well as the negatives of these values.
The largest value of
fo such that all four frequencies shown are integer multiples of fo
equals fo = 2 Hz.
Thus the fundamental cyclic frequency of s(t) is
fo = 2Hz and the fundamental period is To = 1/fo = 0.5 sec.
S 17B.2
______
The sinusoids in s(t) have frequencies
15, 18.75, and 26.25
Hz
The largest value of fo such that all four frequencies shown are
integer multiples of fo is fo = 3.75 Hz.
This is the fundamental
cyclic frequency, and the fundamental period is To = 1/fo = 4/15 sec.
The nonzero complex Fourier series coefficients correspond to
k = 0, (+/)4 , (+/)5 and (+/)7
Using
2*cos(theta) = exp(j*theta) + exp(j*theta)
2*sin(theta) = j*(exp(j*theta)  exp(j*theta))
we have
S_0
=
11
S_4
=
0.5
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S_(4)
=
0.5
S_5
=
j*2.5
S_(5)
=
j*2.5
S_7
= 4.5  j
S_(7)
= 4.5 + j
s(t) is neither odd nor even about t=0.
In the time domain,
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 Spring '08
 staff
 Fourier Series, Fourier series coefficients

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