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037 G
Lv 6
037 G asked in Science & MathematicsMathematics · 1 decade ago

Impulse function?

Use the exponential Fourier series to express periodic impulse function δT = Σδ(t-nT) for n = -∞ to ∞ in terms of exponential Fourier Series Cn.

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  • 1 decade ago
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    By definition Cn = (1/T)*integral[within T](f(t)*exp(-jnwt)*dt),

    and since f(t) = δ(t) it follows Cn = 1/T. Therefore:

    δT = Σ Cn*exp(jnwt) = (1/T)*Σ exp(jnwt) = (1/T)*Σ cos(nwt) [for n = -∞ to ∞] = (1/T) + (2/T)*Σ cos(nwt) [for n = 1 to ∞].

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