Properties of DFT

Before we learn about properties of DFT first we learn about the exact meaning terms of DFT. The Fourier transform can be used for the analysis of a signal. It used for transformation from the time domain to the frequency domain. Here this article gives information about properties of  DFT to know more details or learn about DFT

Linearity : 
Periodic signals : A x(n) + B y(n)
Fourier series coefficients : A ak + B bk

Time shifting :

Periodic signals : x(n - n0)
Fourier series coefficients: ak e-jk(2π/N)n      

Frequency Shifting :

Periodic signals : x(n) ejm(2π/N)n      
Fourier series coefficients : X(k - m) 

Conjugation :
Periodic signals : x*(n)       
Fourier series coefficients : a*-k

Time Reversal :
Periodic signals : x(-n)       
Fourier series coefficients : a-k