Exponential F series?

Question

express periodic impulse delta T = sigma of (delta (t-nT) for n from - to + infinity in terms of exponential Fourier series Cn using exponential Fourier series.

Answer 1

Straightforward. Set:

Sum_n delta(t - nT) = Sum_k=-oo^+oo C_k exp(i 2 pi k t/T)

Multiply both sides by exp(-i 2 pi m t/T) and integrate from -T/2 to T/2 to get the coefficients C_k = 1/T -->

Sum_n delta(t - nT) = (1/T) Sum_k=-oo^+oo exp(i 2 pi k t/T)