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 

Discrete 
time
DTFT : DiscSignals → ContPeriodic2π 
InverseDTFT : ContPeriodic2π → DiscSignals
DFTp : DiscPeriodicp → DiscPeriodicp
InverseDFTp : DiscPeriodicp → DiscPeriodicp