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 a_k + B b_k

Time shifting :

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

Frequency Shifting :

Periodic signals : x(n) e^jm(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

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 a_k + B b_k

Time shifting :

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

Frequency Shifting :

Periodic signals : x(n) e^jm(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