What is DTFT

The DTFT is the member of the Fourier transform family, it can operate on aperiodic, discrete signals. 

The DTFT stands for discrete-time Fourier transform, It is a member of the Fourier transform family that operates on an aperiodic discrete signal. 

The best way to understand the DTFT is how it related to the DFT.  In general, the DTFT is used for the analysis of non-periodic signals. Let us consider the discrete time signal x (n), its DTFT is denoted as X () is given is :

DTFT  = X (Ώ) = e -j Ώn

The inverse DTFT given as :

IDTFT  = X (n) = 1/2∏  * e -j Ώn  d Ώ

In this section, we will also study some  properties of  DTFT to learn better understand this topic. We know that x (n) and X (ω) are Fourier transform pair and is denoted as,

If  x (n)    ↔     X(ω)  

DTFT features :

  • Used for finite and infinite sequence
  • It is only theoretical
  • Cannot be implemented practically
  • DFT is derived from DTFT
  • It is periodic and continuous