EECS20N: Signals and Systems

The Four Fourier Transforms

Below is a summary of the four Fourier transforms.

  Aperiodic time or space 
Continuous frequency
Periodic time or space 
Discrete frequency
Aperiodic frequency 

Continuous time

CTFT: ContSignals → ContSignals
InverseCTFT: ContSignals → ContSignals
FourierSeriesp: ContPeriodicp → DiscSignals
InverseFourierSeriesp : DiscSignals → Periodicp,
Periodic frequency 


DTFT : DiscSignals → ContPeriodic2π 
InverseDTFT : ContPeriodic→ DiscSignals
DFTp : DiscPeriodicp → DiscPeriodicp
InverseDFTp : DiscPeriodicp → DiscPeriodicp