EECS20N: Signals and Systems

Inverse Fourier Transforms

InverseDTFT: ContPeriodic_2π → DiscSignals , such that if x = InverseDTFT (X), then ∀ ν ∈ Reals,

x(n) = (1/2π) ∫_{(− π
to π )} X(ω ) e^{iω n} dω

(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 ∀ ω ∈ Reals,

x(t) = (1/2π) ∫_{(− ∞
to ∞
)} X(ω )e^{iω t} dω

(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.

Week 12