Inverse Fourier Transforms

InverseDTFT: ContPeriodic_2p ® DiscSignals , such that if x = InverseDTFT (X), then " n Î Reals,

x(n) = (1/2p) ò_{(- p
to p )} X(w ) e^{iw n} dw

(This is like a Fourier series expansion, in the that it expresses a signal as a sum (integral) of weighted complex exponentials.)

InverseCTFT: ContSignals ® ContSignals, such that if x = InverseCTFT (X), then " w Î Reals,

x(t) = (1/2p) ò_{(- ¥
to ¥
)} X(w )e^{iw t} dw

(This too is like a Fourier series expansion, in the that it expresses a signal as a sum (integral) of weighted complex exponentials.)

Each of these transforms a frequency-domain representation into a time-domain signal.