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 FourierSeries_p: ContPeriodic_p ® DiscSignals InverseFourierSeries_p : DiscSignals ® Periodic_p,

Periodic frequency
Discrete
time
DTFT : DiscSignals ® ContPeriodic_2p InverseDTFT : ContPeriodic_2p® DiscSignals DFT_p : DiscPeriodic_p ® DiscPeriodic_p InverseDFT_p : DiscPeriodic_p ® DiscPeriodic_p

	Aperiodic time or space Continuous frequency	Periodic time or space Discrete frequency
Aperiodic frequency Continuous time	CTFT: ContSignals ® ContSignals InverseCTFT: ContSignals ® ContSignals	FourierSeries_p: ContPeriodic_p ® DiscSignals InverseFourierSeries_p : DiscSignals ® Periodic_p,
Periodic frequency Discrete time	DTFT : DiscSignals ® ContPeriodic_2p InverseDTFT : ContPeriodic_2p® DiscSignals	DFT_p : DiscPeriodic_p ® DiscPeriodic_p InverseDFT_p : DiscPeriodic_p ® DiscPeriodic_p