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Lecture 8: Properties of the DTFT

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Schedule :: Transforms :: DTFT :: System Analysis :: Properties



  1. $f[-k] \leftrightarrow F(-\Omega)$
  2. $kf[k] \leftrightarrow j \frac{dF(\Omega)}{d\Omega}$
  3. $f[k-k_0] \leftrightarrow F(\Omega) e^{-j k_0 \Omega}$
  4. $f[k] e^{j k \Omega_s} \leftrightarrow F(\Omega - \Omega_s)$
  5. $f_1[k]f_2[k] \leftrightarrow \frac{1}{2\pi} F_1(\Omega)*
F_2(\Omega)$ .
  6. Parseval:

    \begin{displaymath}E_f = \sum_k \vert f[k]\vert^2 = \frac{1}{2\pi} \int_{2\pi}
\vert F(\Omega)\vert^2 d\Omega.
\end{displaymath}
Copyright 2008, by the Contributing Authors. Cite/attribute Resource . admin. (2006, June 05). Lecture 8: Properties of the DTFT. Retrieved January 07, 2011, from Free Online Course Materials — USU OpenCourseWare Web site: http://ocw.usu.edu/Electrical_and_Computer_Engineering/Signals_and_Systems/8_4node4.html. This work is licensed under a Creative Commons License Creative Commons License