Equations > Signal Processing > Fourier Transform Pairs > Discrete-Time Fourier transform of a boxcar sequence

### Discrete-Time Fourier transform of a boxcar sequence

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 $x\left(n\right)=\left\{\begin{array}{c}\hfill 1,0\le n\le N-1\hfill \\ \hfill 0,\mathrm{otherwise}\hfill \end{array}⇔\frac\mathrm{sin}\left(\omega N/2\right)\mathrm{sin}\left(\omega /2\right){e}^{-j\omega \left(N-1\right)/2}$

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