AI Features

Periodicity in Frequency and Time Domains

Discover how a DFT gives rise to a periodic time-domain signal.

Frequency domain

From the DFT definition seen below, the DFT periodicity arises naturally:

X[k]=n=0N1x[n]ej2πkNn,X[k]=\sum_{n=0}^{N-1}x[n]e^{-j2\pi\frac{k}{N}n}, ...