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solved17B

# solved17B - S 17B.1 Using 2*cos(theta = exp(j*theta...

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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+25-30 = 18 -23+25+30 = 32 23-25+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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