DFT

Summary

DFT and inverse DFT

DFT properties

• linear transformation
• periodic
• shift theorem

Concept

Discrete time fourier transform(DTFT)

• discrete time -> continuous frequency

Discrete fourier transform(DFT)

• assumes periodic signals
• discrete time -> discrete frequency

the scaling terms are usually dropped, kinda imprecise “engineering” math
DFT is also slow, the FFT is a fast implementation

Linearity

Periodic frequency domain

• period of

Shift theorem

• shift in one domain -> phase shift in other domain
• assuming periodic signal - wrap around

Symmetry about 0

• complex conjugate

Inverse DFT

• frequency-doamin -> time-domain

scaling is kept as convention