About the Discrete-time Fourier transform (DTFT)

$ \,\mathcal{X}(\omega)=\mathcal{F}(x[n])=\sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}\, $

Practice Problems

• What is the Fourier transform of this DT cosine?
• What is the Fourier transform of this DT rect function?
• Compute the DT Fourier transform of a sinc
• Compute the DT Fourier transform of a rect
• Compute the Fourier transform of 3^n u[-n]
• Compute the Fourier transform of u[n+1]-u[n-2]

Slectures on DTFT

• Definition+properties of Discrete-time Fourier transform (DTFT)
  • Text slecture by Jacob Holtman
  • Text slecture by Fabian Faes
  • Text slecture by Xian Zhang
• Discrete-time Fourier transform (DTFT) of a sampled cosine
  • Text slecture by Andrew Pawling
  • Text slecture by Sutton Hathorn
  • Text slecture by Sahil Sanghani
  • Text slecture by Yijun Han

Other pages related to the DTFT

• Table of discrete-time Fourier transform pairs and properties
• Relationship between DTFT and z-transform
• Graph of DTFT of window function

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Back to table of discrete-time Fourier transform pairs and properties