fs02 - 166 Fourier Series the weight of each impulse...

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the weight of each impulse function equal to the area under a pulse. As a sec ample of calculating Fourier coefficients, we consider a train of impulse tunr ni ,a"i,' Fourier series for an impulse train The Fourier series for the impulse train shown in Figure 4.10 will be calculated. Fron co=+ [x1r1e-ik.,ra1 loJT" trTd2,ll + | E1t1p-i*-,,' 47 = !r-i*.",I : + I oJ-rlz To I f,o t o This result is based on the property of the impulse function l-* rur^, - todt = f(to), 166 Fourier Series Ieq(2.a1)] provided that f(t) is continuous at t : t0. The exponential form of the Fourier series is s x(t) = 3 !,'o'"'. *--1*Tu- A line spectrum for this function is given in Figure 4.11. Because the Fourier coefficie real, no phase plot is given. From (4.13), the c;bined trigonometric form for the trair pulse functions is given by Figure 4.10 Impulse train Figure 4.11 Frequency spectrum t,
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Sec. 4.3 Fourier Series and Frequency Spectra Note that this is also the trigonometric form. A comparison of the frequency spectrum of the square wave (Figure 4.6) with that of the train of impulse functions (Figure 4.11) illustrates an important property of impulse functions. For the square wave, the amplitudes of the har- monics decrease by the factor l"lk,where
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This note was uploaded on 09/22/2009 for the course ECES 302 taught by Professor Carr during the Spring '08 term at Drexel.

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fs02 - 166 Fourier Series the weight of each impulse...

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