EECS20N: Signals and Systems

Fourier Transforms

DTFT: DiscSignals ContPeriodic , such that if X = DTFT (x), then ∀ ωReals,

X(ω) = (m = − ∞ to ∞ ) x(m)e−imω

To verify that this is periodic with period 2π, just evaluate X(ω + 2π) to show that it is equal to X(ω) for all ω.


CTFT: ContSignals ContSignals, such that if X = CTFT (x), then ∀ ωReals,

X(ω) = (− ∞ to ∞ ) x(t)e−iω t dt


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