Yahoo Answers is shutting down on May 4th, 2021 (Eastern Time) and beginning April 20th, 2021 (Eastern Time) the Yahoo Answers website will be in read-only mode. There will be no changes to other Yahoo properties or services, or your Yahoo account. You can find more information about the Yahoo Answers shutdown and how to download your data on this help page.
Trending News
Promoted
037 G
Lv 6
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.
1 Answer
Relevance
- fernando_007Lv 61 decade agoFavorite Answer
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 ∞].
Still have questions? Get your answers by asking now.