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Table of Discrete-Time Fourier Transform Pairs
pfister.ee.duke.eduTable of Discrete-Time Fourier Transform Pairs: Discrete-Time Fourier Transform : X() = X1 n=1 x[n]e j n Inverse Discrete-Time Fourier Transform : x[n] = 1 2ˇ Z 2ˇ X()ej td: x[n] X() condition anu[n] 1 1 ae j jaj<1 (n+ 1)anu[n] 1 (1 ae j)2 jaj<1 (n+ r 1)! n!(r 1)! anu[n] 1 (1 ae j)r jaj<1 [n] 1 [n n 0] e j n 0 x[n] = 1 2ˇ X1 k=1 (2ˇk) u[n ...
Lecture 11: Discrete-time Fourier transform
ocw.mit.edutween the time and frequency domains and in fact the Fourier transform of the Fourier transform gets us back to the original signal, time-reversed. In discrete time the situation is the opposite. The Fourier series represents a pe-riodic time-domain sequence by a periodic sequence of Fourier series coeffi-cients.